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paretotails


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statistics: paretotails

Piecewise distribution with generalized Pareto tails.

A paretotails object is a piecewise probability distribution fit to
sample data. A generalized Pareto distribution (GPD) is fit to each tail
of the data, below a lower quantile and above an upper quantile, while the
middle of the distribution is described by the empirical cumulative
distribution function of the data. This gives a smooth model for the
tails, useful for extreme value analysis, together with a nonparametric
description of the central region.

Create a paretotails object with the constructor
pt = paretotails ( x , pl , pu ) , where x
is the sample data and pl and pu are the cumulative
probabilities at the lower and upper tail boundaries. Data at or below the
pl quantile form the lower tail, data at or above the pu
quantile form the upper tail, and the rest form the middle segment.

Query the fitted object with the methods cdf , pdf ,
icdf , random , boundary , nsegments ,
segment , lowerparams , and upperparams .

Note: the kernel-smoothed middle option of MATLAB
( paretotails ( x , pl , pu , "kernel") ) is not yet
supported; only the default empirical ( "ecdf" ) middle is available.

See also:
gpfit,
gpcdf,
gppdf,
gpinv,
ecdf,
fitdist,
GeneralizedParetoDistribution


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Piecewise distribution with generalized Pareto tails.



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paretotails.NumParameters


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paretotails: property NumParameters

Number of estimated parameters (two per fitted generalized Pareto tail).


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Number of estimated parameters (two per fitted generalized Pareto tail).



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paretotails.NumSegments


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paretotails: property NumSegments

Number of segments in the piecewise distribution (a lower tail, a middle,
and an upper tail give three).


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Number of segments in the piecewise distribution (a lower tail, a middle, and an upper tail give three).



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paretotails.boundary


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paretotails: [ p , q ] = boundary ( pt )

Boundary probabilities p and quantiles q of the segments of
the paretotails object pt , as column vectors.


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Boundary probabilities p and quantiles q of the segments of the paretotails object pt, as column vectors.



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paretotails.cdf


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paretotails: p = cdf ( pt , x )

Cumulative distribution function of the paretotails object
pt evaluated at the values in x .


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Cumulative distribution function of the paretotails object pt evaluated at the values in x.



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paretotails.icdf


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paretotails: x = icdf ( pt , p )

Inverse cumulative distribution function (quantile function) of the
paretotails object pt evaluated at the probabilities
p .


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Inverse cumulative distribution function (quantile function) of the paretotails object pt evaluated at the probabilities p.



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paretotails.lowerparams


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paretotails: params = lowerparams ( pt )

Shape and scale parameters [ k , sigma ] of the
generalized Pareto distribution fit to the lower tail of pt .


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Shape and scale parameters [k, sigma] of the generalized Pareto distribution fit to the lower tail of pt.



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paretotails.nsegments


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paretotails: n = nsegments ( pt )

Number of segments in the paretotails object pt .


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Number of segments in the paretotails object pt.



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paretotails.paretotails


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paretotails: pt = paretotails ( x , pl , pu )
paretotails: pt = paretotails ( x , pl , pu , cdffun )

Fit a piecewise distribution with generalized Pareto tails to x .

pl and pu are the cumulative probabilities of the lower and
upper tail boundaries, with 0 <= pl < pu <= 1 . A
generalized Pareto distribution is fit by maximum likelihood to the
exceedances in each tail; the middle segment uses the empirical
cumulative distribution of x .

cdffun selects the middle segment and defaults to "ecdf" ;
the "kernel" option of MATLAB is not yet supported.


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Fit a piecewise distribution with generalized Pareto tails to x.



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paretotails.pdf


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paretotails: y = pdf ( pt , x )

Probability density function of the paretotails object pt
evaluated at the values in x .


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Probability density function of the paretotails object pt evaluated at the values in x.



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paretotails.random


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paretotails: r = random ( pt )
paretotails: r = random ( pt , sz )
paretotails: r = random ( pt , m , n , &hellip;)

Random values drawn from the paretotails object pt , by
inverse transform sampling. The size arguments follow rand .


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Random values drawn from the paretotails object pt, by inverse transform sampling.



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paretotails.segment


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paretotails: s = segment ( pt , x , p )

Segment indices for the paretotails object pt . Supply the
data values in x (with p empty) or the cumulative
probabilities in p (with x empty). Segment 1 is the
lower tail, 2 the middle, and 3 the upper tail.


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Segment indices for the paretotails object pt.



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paretotails.upperparams


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paretotails: params = upperparams ( pt )

Shape and scale parameters [ k , sigma ] of the
generalized Pareto distribution fit to the upper tail of pt .


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Shape and scale parameters [k, sigma] of the generalized Pareto distribution fit to the upper tail of pt.



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prob.BetaDistribution


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statistics: prob.BetaDistribution

Beta probability distribution object.

A prob.BetaDistribution object consists of parameters, a model
description, and sample data for a beta probability distribution.

The beta distribution is a family of continuous probability distributions
defined on the interval [0, 1] in terms of two positive parameters,
denoted by alpha ( a ) and beta ( b ) , that appear
as exponents of the variable and its complement to 1, respectively, and
control the shape of the distribution.

There are several ways to create a prob.BetaDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.BetaDistribution ( a , b )
to create a beta distribution with fixed parameter values a and
b .
Use the static method prob.BetaDistribution.fit ( x ,
alpha , freq , options ) to fit a distribution to the data
in x using the same input arguments as the betafit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the beta distribution can be found at
https://en.wikipedia.org/wiki/Beta_distribution

See also:
fitdist,
makedist,
betacdf,
betainv,
betapdf,
betarnd,
betafit,
betalike,
betastat


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Beta probability distribution object.



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prob.BetaDistribution.BetaDistribution


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prob.BetaDistribution: pd = BetaDistribution ( a , b )
prob.BetaDistribution: pd = BetaDistribution ()

Create a prob.BetaDistribution object.

a and b are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
a 1 and b 1.

makedist is the usual way to create a distribution object.


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Create a prob.BetaDistribution object.



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prob.BetaDistribution.DistributionName


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prob.BetaDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


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Probability distribution name



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prob.BetaDistribution.InputData


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prob.BetaDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : an empty array, since prob.BetaDistribution does
not allow censoring.
frequency : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


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Data used for fitting a probability distribution



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prob.BetaDistribution.IsTruncated


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prob.BetaDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


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Flag for truncated probability distribution



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prob.BetaDistribution.NumParameters


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prob.BetaDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


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Number of parameters



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prob.BetaDistribution.ParameterCovariance


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prob.BetaDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


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Covariance matrix of the parameter estimates



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prob.BetaDistribution.ParameterDescription


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prob.BetaDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


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Description of parameters



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prob.BetaDistribution.ParameterIsFixed


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prob.BetaDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


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Flag for fixed parameters



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prob.BetaDistribution.ParameterNames


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prob.BetaDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
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Names of parameters



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prob.BetaDistribution.ParameterValues


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prob.BetaDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the a and b
properties.


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Distribution parameter values



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prob.BetaDistribution.Truncation


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prob.BetaDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


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Truncation interval



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prob.BetaDistribution.a


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prob.BetaDistribution: property a

First shape parameter

A positive scalar value characterizing the shape of the beta
distribution. You can access the a property using dot name
assignment.


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First shape parameter



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prob.BetaDistribution.b


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prob.BetaDistribution: property b

Second shape parameter

A positive scalar value characterizing the shape of the beta
distribution. You can access the b property using dot name
assignment.


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Second shape parameter



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prob.BetaDistribution.cdf


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prob.BetaDistribution: p = cdf ( pd , x )
prob.BetaDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



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prob.BetaDistribution.icdf


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prob.BetaDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


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Compute the inverse cumulative distribution function (iCDF).



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prob.BetaDistribution.iqr


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prob.BetaDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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Compute the interquartile range of a probability distribution.



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prob.BetaDistribution.mean


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prob.BetaDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


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Compute the mean of a probability distribution.



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prob.BetaDistribution.median


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prob.BetaDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


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Compute the median of a probability distribution.



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prob.BetaDistribution.negloglik


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prob.BetaDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood
of the probability distribution object, pd .


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Compute the negative loglikelihood of a probability distribution.



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prob.BetaDistribution.paramci


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prob.BetaDistribution: ci = paramci ( pd )
prob.BetaDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.BetaDistribution.pdf


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prob.BetaDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


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Compute the probability distribution function (PDF).



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prob.BetaDistribution.plot


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prob.BetaDistribution: plot ( pd )
prob.BetaDistribution: plot ( pd , Name , Value )
prob.BetaDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


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Plot a probability distribution object.



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prob.BetaDistribution.proflik


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prob.BetaDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.BetaDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.BetaDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.BetaDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.BetaDistribution: [ nlogL , param ] = proflik ( pd )
prob.BetaDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the beta distribution, pnum = 1 selects the parameter
a and pnum = 2 selects the parameter b .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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# length: 28
prob.BetaDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 698
prob.BetaDistribution: r = random ( pd )
prob.BetaDistribution: r = random ( pd , rows )
prob.BetaDistribution: r = random ( pd , rows , cols , &hellip;)
prob.BetaDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BetaDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.BetaDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BetaDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 543
prob.BetaDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BetaDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.BetaDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1295
statistics: prob.BinomialDistribution

Binomial probability distribution object.

A prob.BinomialDistribution object consists of parameters, a model
description, and sample data for a binomial probability distribution.

The binomial distribution is a discrete probability distribution that
models the number of successes in a sequence of N independent trials,
each with a probability of success p .

There are several ways to create a prob.BinomialDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.BinomialDistribution ( N , p )
to create a binomial distribution with fixed parameter values N and
p .
Use the static method prob.BinomialDistribution.fit ( x ,
ntrials , alpha ) to fit a distribution to the data in x
using the same input arguments as the binofit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the binomial distribution can be found at
https://en.wikipedia.org/wiki/Binomial_distribution

See also:
fitdist,
makedist,
binocdf,
binoinv,
binopdf,
binornd,
binofit,
binolike,
binostat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Binomial probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.BinomialDistribution.BinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 372
prob.BinomialDistribution: pd = BinomialDistribution ( N , p )
prob.BinomialDistribution: pd = BinomialDistribution ()

Create a prob.BinomialDistribution object.

N and p are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
N 1 and p 0.5.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
Create a prob.BinomialDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BinomialDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.BinomialDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.BinomialDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 577
prob.BinomialDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : an empty array, since prob.BinomialDistribution
does not allow censoring.
frequency : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BinomialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.BinomialDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.BinomialDistribution.N


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.BinomialDistribution: property N

Number of trials

A positive integer value characterizing the number of trials in the
binomial distribution. You can access the N property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
Number of trials



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.BinomialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.BinomialDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.BinomialDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 622
prob.BinomialDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.BinomialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.BinomialDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BinomialDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 290
prob.BinomialDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.BinomialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.BinomialDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BinomialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 286
prob.BinomialDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the N and p
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.BinomialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 354
prob.BinomialDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 407
prob.BinomialDistribution: p = cdf ( pd , x )
prob.BinomialDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BinomialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 252
prob.BinomialDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.BinomialDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BinomialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.BinomialDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.BinomialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.BinomialDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.BinomialDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.BinomialDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood
of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.BinomialDistribution.p


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 240
prob.BinomialDistribution: property p

Probability of success

A scalar value in the range [0, 1] characterizing the probability
of success in each trial of the binomial distribution. You can access
the p property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
Probability of success



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BinomialDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 992
prob.BinomialDistribution: ci = paramci ( pd )
prob.BinomialDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.BinomialDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BinomialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1548
prob.BinomialDistribution: plot ( pd )
prob.BinomialDistribution: plot ( pd , Name , Value )
prob.BinomialDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BinomialDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2133
prob.BinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.BinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.BinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.BinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.BinomialDistribution: [ nlogL , param ] = proflik ( pd )
prob.BinomialDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the binomial distribution, pnum = 1 selects the
parameter N and pnum = 2 selects the parameter
p .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.BinomialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 714
prob.BinomialDistribution: r = random ( pd )
prob.BinomialDistribution: r = random ( pd , rows )
prob.BinomialDistribution: r = random ( pd , rows , cols , &hellip;)
prob.BinomialDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, binornd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.BinomialDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.BinomialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 547
prob.BinomialDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.BinomialDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BirnbaumSaundersDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1455
statistics: prob.BirnbaumSaundersDistribution

Birnbaum-Saunders probability distribution object.

A prob.BirnbaumSaundersDistribution object consists of parameters, a
model description, and sample data for a Birnbaum-Saunders probability
distribution.

The Birnbaum-Saunders distribution is a continuous probability distribution
that models the time to failure of materials subjected to cyclic loading.
It is defined by scale parameter beta and shape parameter
gamma .

There are several ways to create a prob.BirnbaumSaundersDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.BirnbaumSaundersDistribution ( beta ,
gamma ) to create a Birnbaum-Saunders distribution with fixed
parameter values beta and gamma .
Use the static method prob.BirnbaumSaundersDistribution.fit
( x , alpha , censor , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
bisafit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Birnbaum-Saunders distribution can be found
at
https://en.wikipedia.org/wiki/Birnbaum%E2%80%93Saunders_distribution

See also:
fitdist,
makedist,
bisacdf,
bisainv,
bisapdf,
bisarnd,
bisafit,
bisalike,
bisastat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Birnbaum-Saunders probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
prob.BirnbaumSaundersDistribution.BirnbaumSaundersDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 431
prob.BirnbaumSaundersDistribution: pd = BirnbaumSaundersDistribution ( beta , gamma )
prob.BirnbaumSaundersDistribution: pd = BirnbaumSaundersDistribution ()

Create a prob.BirnbaumSaundersDistribution object.

beta and gamma are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, beta 1 and gamma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Create a prob.BirnbaumSaundersDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.BirnbaumSaundersDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.BirnbaumSaundersDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.BirnbaumSaundersDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 749
prob.BirnbaumSaundersDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.BirnbaumSaundersDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.BirnbaumSaundersDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.BirnbaumSaundersDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.BirnbaumSaundersDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
prob.BirnbaumSaundersDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 631
prob.BirnbaumSaundersDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.BirnbaumSaundersDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 242
prob.BirnbaumSaundersDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.BirnbaumSaundersDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 298
prob.BirnbaumSaundersDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.BirnbaumSaundersDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.BirnbaumSaundersDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.BirnbaumSaundersDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 301
prob.BirnbaumSaundersDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the beta and gamma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.BirnbaumSaundersDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 362
prob.BirnbaumSaundersDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.beta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.BirnbaumSaundersDistribution: property beta

Scale parameter

A positive scalar value characterizing the scale of the
Birnbaum-Saunders distribution. You can access the beta
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 423
prob.BirnbaumSaundersDistribution: p = cdf ( pd , x )
prob.BirnbaumSaundersDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.BirnbaumSaundersDistribution.gamma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 216
prob.BirnbaumSaundersDistribution: property gamma

Shape parameter

A positive scalar value characterizing the shape of the
Birnbaum-Saunders distribution. You can access the gamma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 260
prob.BirnbaumSaundersDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.BirnbaumSaundersDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.BirnbaumSaundersDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.BirnbaumSaundersDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
prob.BirnbaumSaundersDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.BirnbaumSaundersDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.BirnbaumSaundersDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BirnbaumSaundersDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1008
prob.BirnbaumSaundersDistribution: ci = paramci ( pd )
prob.BirnbaumSaundersDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 220
prob.BirnbaumSaundersDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1572
prob.BirnbaumSaundersDistribution: plot ( pd )
prob.BirnbaumSaundersDistribution: plot ( pd , Name , Value )
prob.BirnbaumSaundersDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BirnbaumSaundersDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2197
prob.BirnbaumSaundersDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.BirnbaumSaundersDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.BirnbaumSaundersDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.BirnbaumSaundersDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.BirnbaumSaundersDistribution: [ nlogL , param ] = proflik ( pd )
prob.BirnbaumSaundersDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Birnbaum-Saunders distribution, pnum = 1 selects
the parameter beta and pnum = 2 selects the
parameter gamma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.BirnbaumSaundersDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 746
prob.BirnbaumSaundersDistribution: r = random ( pd )
prob.BirnbaumSaundersDistribution: r = random ( pd , rows )
prob.BirnbaumSaundersDistribution: r = random ( pd , rows , cols , &hellip;)
prob.BirnbaumSaundersDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, bisarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.BirnbaumSaundersDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BirnbaumSaundersDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 555
prob.BirnbaumSaundersDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 185
prob.BirnbaumSaundersDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
prob.BurrDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1334
statistics: prob.BurrDistribution

Burr probability distribution object.

A prob.BurrDistribution object consists of parameters, a model
description, and sample data for a Burr probability distribution.

The Burr distribution is a continuous probability distribution that models
a non-negative random variable, commonly used to model household income.
It is defined by a scale parameter alpha and two shape parameters
c and k .

There are several ways to create a prob.BurrDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.BurrDistribution ( alpha , c ,
k ) to create a Burr distribution with fixed parameter values
alpha , c , and k .
Use the static method prob.BurrDistribution.fit ( x ,
alpha , censor , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
burrfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Burr distribution can be found at
https://en.wikipedia.org/wiki/Burr_distribution

See also:
fitdist,
makedist,
burrcdf,
burrinv,
burrpdf,
burrrnd,
burrfit,
burrlike,
burrstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
Burr probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BurrDistribution.BurrDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 375
prob.BurrDistribution: pd = BurrDistribution ( alpha , c , k )
prob.BurrDistribution: pd = BurrDistribution ()

Create a prob.BurrDistribution object.

alpha , c and k are the distribution parameters, which
the class help describes. Called with no arguments the parameters take
their defaults, alpha 1, c 1 and k 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Create a prob.BurrDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BurrDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
prob.BurrDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.BurrDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 564
prob.BurrDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : an empty array, since prob.BurrDistribution does
not allow censoring.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BurrDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.BurrDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.BurrDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.BurrDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BurrDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 619
prob.BurrDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 3&times;3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BurrDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 230
prob.BurrDistribution: property ParameterDescription

Description of parameters

A 3&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BurrDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 286
prob.BurrDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.BurrDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.BurrDistribution: property ParameterNames

Names of parameters

A 3&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BurrDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 292
prob.BurrDistribution: property ParameterValues

Distribution parameter values

A 3&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the alpha , c , and
k properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.BurrDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 350
prob.BurrDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.BurrDistribution.alpha


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.BurrDistribution: property alpha

Scale parameter

A positive scalar value characterizing the scale of the Burr
distribution. You can access the alpha property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.BurrDistribution.c


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.BurrDistribution: property c

First shape parameter

A positive scalar value characterizing the first shape parameter of the
Burr distribution. You can access the c property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
First shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BurrDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 399
prob.BurrDistribution: p = cdf ( pd , x )
prob.BurrDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.BurrDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 248
prob.BurrDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BurrDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.BurrDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.BurrDistribution.k


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.BurrDistribution: property k

Second shape parameter

A positive scalar value characterizing the second shape parameter of the
Burr distribution. You can access the k property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
Second shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.BurrDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 167
prob.BurrDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.BurrDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.BurrDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.BurrDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 221
prob.BurrDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BurrDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 984
prob.BurrDistribution: ci = paramci ( pd )
prob.BurrDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BurrDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.BurrDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.BurrDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1536
prob.BurrDistribution: plot ( pd )
prob.BurrDistribution: plot ( pd , Name , Value )
prob.BurrDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
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# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BurrDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2146
prob.BurrDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.BurrDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.BurrDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.BurrDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.BurrDistribution: [ nlogL , param ] = proflik ( pd )
prob.BurrDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Burr distribution, pnum = 1 selects the parameter
alpha , pnum = 2 selects the parameter c ,
and pnum = 3 selects the parameter k .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.BurrDistribution.random


# name: <cell-element>
# type: sq_string
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# length: 698
prob.BurrDistribution: r = random ( pd )
prob.BurrDistribution: r = random ( pd , rows )
prob.BurrDistribution: r = random ( pd , rows , cols , &hellip;)
prob.BurrDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, burrrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BurrDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.BurrDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BurrDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 543
prob.BurrDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BurrDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.BurrDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.ExponentialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1296
statistics: prob.ExponentialDistribution

Exponential probability distribution object.

A prob.ExponentialDistribution object consists of parameters, a model
description, and sample data for a exponential probability distribution.

The exponential distribution is a continuous probability distribution with
mean parameter mu that models the time between events in a Poisson
process.

There are several ways to create a prob.ExponentialDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.ExponentialDistribution ( mu )
to create a exponential distribution with fixed parameter value mu .
Use the static method prob.ExponentialDistribution.fit ( x ,
alpha , censor , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
expfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the exponential distribution can be found at
https://en.wikipedia.org/wiki/Exponential_distribution

See also:
fitdist,
makedist,
expcdf,
expinv,
exppdf,
exprnd,
expfit,
explike,
expstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Exponential probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.ExponentialDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.ExponentialDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.ExponentialDistribution.ExponentialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 365
prob.ExponentialDistribution: pd = ExponentialDistribution ( mu )
prob.ExponentialDistribution: pd = ExponentialDistribution ()

Create a prob.ExponentialDistribution object.

mu is the distribution parameter, which the class help describes.
Called with no arguments the parameter takes its default, mu 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
Create a prob.ExponentialDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.ExponentialDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 744
prob.ExponentialDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.ExponentialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.ExponentialDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.ExponentialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.ExponentialDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.ExponentialDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 454
prob.ExponentialDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A scalar numeric value containing the variance-covariance of the
parameter estimate. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then the variance-covariance is zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.ExponentialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 237
prob.ExponentialDistribution: property ParameterDescription

Description of parameters

A 1&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.ExponentialDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 284
prob.ExponentialDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;1 logical vector specifying whether the parameter is fixed or
estimated. true value corresponds to fixed parameter,
false value corresponds to parameter estimate. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.ExponentialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.ExponentialDistribution: property ParameterNames

Names of parameters

A 1&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.ExponentialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 280
prob.ExponentialDistribution: property ParameterValues

Distribution parameter values

A 1&times;1 numeric vector containing the value of the distribution
parameter. This property is read-only. You can change the distribution
parameter by assigning a new value to the mu
property.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.ExponentialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 357
prob.ExponentialDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 413
prob.ExponentialDistribution: p = cdf ( pd , x )
prob.ExponentialDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExponentialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 255
prob.ExponentialDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.ExponentialDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExponentialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 174
prob.ExponentialDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.ExponentialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 182
prob.ExponentialDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.ExponentialDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.ExponentialDistribution: property mu

Mean parameter

A positive scalar value characterizing the mean of the
exponential distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
Mean parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.ExponentialDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 228
prob.ExponentialDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExponentialDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 998
prob.ExponentialDistribution: ci = paramci ( pd )
prob.ExponentialDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 215
prob.ExponentialDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExponentialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1557
prob.ExponentialDistribution: plot ( pd )
prob.ExponentialDistribution: plot ( pd , Name , Value )
prob.ExponentialDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExponentialDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2118
prob.ExponentialDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.ExponentialDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.ExponentialDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.ExponentialDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.ExponentialDistribution: [ nlogL , param ] = proflik ( pd )
prob.ExponentialDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the exponential distribution, pnum = 1 selects the
parameter mu .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.ExponentialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 726
prob.ExponentialDistribution: r = random ( pd )
prob.ExponentialDistribution: r = random ( pd , rows )
prob.ExponentialDistribution: r = random ( pd , rows , cols , &hellip;)
prob.ExponentialDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.ExponentialDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.ExponentialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 550
prob.ExponentialDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 180
prob.ExponentialDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.ExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1410
statistics: prob.ExtremeValueDistribution

Extreme value probability distribution object.

A prob.ExtremeValueDistribution object consists of parameters, a model
description, and sample data for an extreme value probability distribution.

The extreme value distribution is also known as the Gumbel distribution for
maxima, and it is a limiting distribution for the maximum of a large number
of samples from a continuous distribution. It is defined by location
parameter mu and scale parameter sigma .

There are several ways to create a prob.ExtremeValueDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with specified parameter values using the
makedist function.
Use the constructor prob.ExtremeValueDistribution ( mu ,
sigma ) to create an extreme value distribution with specified
parameter values.
Use the static method prob.ExtremeValueDistribution.fit ( x ,
alpha , censor , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
evfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the
constructor and the aforementioned static method.

Further information about the Gumbel distribution can be found at
https://en.wikipedia.org/wiki/Gumbel_distribution

See also:
fitdist,
makedist,
evcdf,
evinv,
evpdf,
evrnd,
evfit,
evlike,
evstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Extreme value probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.ExtremeValueDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.ExtremeValueDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.ExtremeValueDistribution.ExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 405
prob.ExtremeValueDistribution: pd = ExtremeValueDistribution ( mu , sigma )
prob.ExtremeValueDistribution: pd = ExtremeValueDistribution ()

Create a prob.ExtremeValueDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Create a prob.ExtremeValueDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.ExtremeValueDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 745
prob.ExtremeValueDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.ExtremeValueDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 215
prob.ExtremeValueDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.ExtremeValueDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.ExtremeValueDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.ExtremeValueDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 627
prob.ExtremeValueDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.ExtremeValueDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 238
prob.ExtremeValueDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.ExtremeValueDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.ExtremeValueDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.ExtremeValueDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 215
prob.ExtremeValueDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.ExtremeValueDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 295
prob.ExtremeValueDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.ExtremeValueDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 358
prob.ExtremeValueDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 415
prob.ExtremeValueDistribution: p = cdf ( pd , x )
prob.ExtremeValueDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.ExtremeValueDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 256
prob.ExtremeValueDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.ExtremeValueDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.ExtremeValueDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.ExtremeValueDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExtremeValueDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 183
prob.ExtremeValueDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExtremeValueDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.ExtremeValueDistribution: property mu

Location parameter

A scalar value characterizing the location of the
extreme value distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.ExtremeValueDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 229
prob.ExtremeValueDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.ExtremeValueDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1000
prob.ExtremeValueDistribution: ci = paramci ( pd )
prob.ExtremeValueDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 216
prob.ExtremeValueDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.ExtremeValueDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1560
prob.ExtremeValueDistribution: plot ( pd )
prob.ExtremeValueDistribution: plot ( pd , Name , Value )
prob.ExtremeValueDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.ExtremeValueDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2167
prob.ExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.ExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.ExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.ExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.ExtremeValueDistribution: [ nlogL , param ] = proflik ( pd )
prob.ExtremeValueDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the extreme value distribution, pnum = 1 selects the
parameter mu and pnum = 2 selects the parameter
sigma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExtremeValueDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 730
prob.ExtremeValueDistribution: r = random ( pd )
prob.ExtremeValueDistribution: r = random ( pd , rows )
prob.ExtremeValueDistribution: r = random ( pd , rows , cols , &hellip;)
prob.ExtremeValueDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.ExtremeValueDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.ExtremeValueDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the
extreme value distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.ExtremeValueDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.ExtremeValueDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 551
prob.ExtremeValueDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 181
prob.ExtremeValueDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
prob.GammaDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1263
statistics: prob.GammaDistribution

Gamma probability distribution object.

A prob.GammaDistribution object consists of parameters, a model
description, and sample data for a gamma probability distribution.

The gamma distribution is a continuous probability distribution that models
the time to failure of a process. It is defined by shape parameter a
and scale parameter b .

There are several ways to create a prob.GammaDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.GammaDistribution ( a , b )
to create a gamma distribution with fixed parameter values a and
b .
Use the static method prob.GammaDistribution.fit ( x ,
alpha , censor , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
gamfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the gamma distribution can be found at
https://en.wikipedia.org/wiki/Gamma_distribution

See also:
fitdist,
makedist,
gamcdf,
gaminv,
gampdf,
gamrnd,
gamfit,
gamlike,
gamstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Gamma probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GammaDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.GammaDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GammaDistribution.GammaDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 355
prob.GammaDistribution: pd = GammaDistribution ( a , b )
prob.GammaDistribution: pd = GammaDistribution ()

Create a prob.GammaDistribution object.

a and b are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
a 1 and b 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Create a prob.GammaDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.GammaDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 738
prob.GammaDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.GammaDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.GammaDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.GammaDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.GammaDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GammaDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 620
prob.GammaDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.GammaDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 231
prob.GammaDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GammaDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
prob.GammaDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.GammaDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.GammaDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GammaDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 283
prob.GammaDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the a and b
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.GammaDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 351
prob.GammaDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.GammaDistribution.a


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 185
prob.GammaDistribution: property a

Shape parameter

A positive scalar value characterizing the shape of the
gamma distribution. You can access the a
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.GammaDistribution.b


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 185
prob.GammaDistribution: property b

Scale parameter

A positive scalar value characterizing the scale of the
gamma distribution. You can access the b
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 401
prob.GammaDistribution: p = cdf ( pd , x )
prob.GammaDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.GammaDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 249
prob.GammaDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.GammaDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.GammaDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 168
prob.GammaDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.GammaDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 176
prob.GammaDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.GammaDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 222
prob.GammaDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.GammaDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 986
prob.GammaDistribution: ci = paramci ( pd )
prob.GammaDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.GammaDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.GammaDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1539
prob.GammaDistribution: plot ( pd )
prob.GammaDistribution: plot ( pd , Name , Value )
prob.GammaDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.GammaDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2112
prob.GammaDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.GammaDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.GammaDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.GammaDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.GammaDistribution: [ nlogL , param ] = proflik ( pd )
prob.GammaDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the gamma distribution, pnum = 1 selects the parameter
a and pnum = 2 selects the parameter b .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.GammaDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 701
prob.GammaDistribution: r = random ( pd )
prob.GammaDistribution: r = random ( pd , rows )
prob.GammaDistribution: r = random ( pd , rows , cols , &hellip;)
prob.GammaDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, gamrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.GammaDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.GammaDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 544
prob.GammaDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 174
prob.GammaDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GeneralizedExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1496
statistics: prob.GeneralizedExtremeValueDistribution

Generalized extreme value probability distribution object.

A prob.GeneralizedExtremeValueDistribution object consists of parameters,
a model description, and sample data for a generalized extreme value
probability distribution.

The generalized extreme value distribution is a continuous probability
distribution that models extreme values. It is defined by shape parameter
k , scale parameter sigma , and location parameter mu .

There are several ways to create a
prob.GeneralizedExtremeValueDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.GeneralizedExtremeValueDistribution
( k , sigma , mu ) to create a generalized extreme value
distribution with fixed parameter values k , sigma , and
mu .
Use the static method prob.GeneralizedExtremeValueDistribution.fit
( x , alpha , freq , options ) to fit a distribution to
the data in x using the same input arguments as the gevfit
function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the generalized extreme value distribution can be
found at
https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution

See also:
fitdist,
makedist,
gevcdf,
gevinv,
gevpdf,
gevrnd,
gevfit,
gevlike,
gevstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
Generalized extreme value probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
prob.GeneralizedExtremeValueDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.GeneralizedExtremeValueDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 76
prob.GeneralizedExtremeValueDistribution.GeneralizedExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 473
prob.GeneralizedExtremeValueDistribution: pd = GeneralizedExtremeValueDistribution ( k , sigma , mu )
prob.GeneralizedExtremeValueDistribution: pd = GeneralizedExtremeValueDistribution ()

Create a prob.GeneralizedExtremeValueDistribution object.

k , sigma and mu are the distribution parameters, which
the class help describes. Called with no arguments the parameters take
their defaults, k 0, sigma 1 and mu 0.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
Create a prob.GeneralizedExtremeValueDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.GeneralizedExtremeValueDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 756
prob.GeneralizedExtremeValueDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.GeneralizedExtremeValueDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.GeneralizedExtremeValueDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.GeneralizedExtremeValueDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.GeneralizedExtremeValueDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
prob.GeneralizedExtremeValueDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 638
prob.GeneralizedExtremeValueDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 3&times;3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
prob.GeneralizedExtremeValueDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 249
prob.GeneralizedExtremeValueDistribution: property ParameterDescription

Description of parameters

A 3&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
prob.GeneralizedExtremeValueDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 305
prob.GeneralizedExtremeValueDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
prob.GeneralizedExtremeValueDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.GeneralizedExtremeValueDistribution: property ParameterNames

Names of parameters

A 3&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
prob.GeneralizedExtremeValueDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 312
prob.GeneralizedExtremeValueDistribution: property ParameterValues

Distribution parameter values

A 3&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the k , sigma , and
mu properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.GeneralizedExtremeValueDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 369
prob.GeneralizedExtremeValueDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 437
prob.GeneralizedExtremeValueDistribution: p = cdf ( pd , x )
prob.GeneralizedExtremeValueDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedExtremeValueDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 267
prob.GeneralizedExtremeValueDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.GeneralizedExtremeValueDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GeneralizedExtremeValueDistribution.k


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.GeneralizedExtremeValueDistribution: property k

Shape parameter

A scalar value characterizing the shape of the generalized extreme value
distribution. You can access the k property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedExtremeValueDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 186
prob.GeneralizedExtremeValueDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.GeneralizedExtremeValueDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.GeneralizedExtremeValueDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.GeneralizedExtremeValueDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 222
prob.GeneralizedExtremeValueDistribution: property mu

Location parameter

A scalar value characterizing the location of the generalized extreme
value distribution. You can access the mu property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.GeneralizedExtremeValueDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 240
prob.GeneralizedExtremeValueDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.GeneralizedExtremeValueDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1022
prob.GeneralizedExtremeValueDistribution: ci = paramci ( pd )
prob.GeneralizedExtremeValueDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 227
prob.GeneralizedExtremeValueDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedExtremeValueDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1593
prob.GeneralizedExtremeValueDistribution: plot ( pd )
prob.GeneralizedExtremeValueDistribution: plot ( pd , Name , Value )
prob.GeneralizedExtremeValueDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.GeneralizedExtremeValueDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2282
prob.GeneralizedExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.GeneralizedExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.GeneralizedExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.GeneralizedExtremeValueDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.GeneralizedExtremeValueDistribution: [ nlogL , param ] = proflik ( pd )
prob.GeneralizedExtremeValueDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the generalized extreme value distribution, pnum = 1
selects the parameter k , pnum = 2 selects the
parameter sigma , and pnum = 3 selects the
parameter mu .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.GeneralizedExtremeValueDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 773
prob.GeneralizedExtremeValueDistribution: r = random ( pd )
prob.GeneralizedExtremeValueDistribution: r = random ( pd , rows )
prob.GeneralizedExtremeValueDistribution: r = random ( pd , rows , cols , &hellip;)
prob.GeneralizedExtremeValueDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, gevrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.GeneralizedExtremeValueDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 231
prob.GeneralizedExtremeValueDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the generalized
extreme value distribution. You can access the sigma property
using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.GeneralizedExtremeValueDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.GeneralizedExtremeValueDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 562
prob.GeneralizedExtremeValueDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.GeneralizedExtremeValueDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.GeneralizedParetoDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1501
statistics: prob.GeneralizedParetoDistribution

Generalized Pareto probability distribution object.

A prob.GeneralizedParetoDistribution object consists of parameters, a
model description, and sample data for a Generalized Pareto probability
distribution.

The Generalized Pareto distribution is a continuous probability
distribution that models the tail behavior of other distributions, commonly
used for extreme value analysis. It is defined by shape parameter k ,
scale parameter sigma , and location parameter theta .

There are several ways to create a prob.GeneralizedParetoDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.GeneralizedParetoDistribution ( k ,
sigma , theta ) to create a Generalized Pareto distribution with
fixed parameter values k , sigma , and theta .
Use the static method prob.GeneralizedParetoDistribution.fit
( x , theta , alpha , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
gpfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Generalized Pareto distribution can be found
at
https://en.wikipedia.org/wiki/Generalized_Pareto_distribution

See also:
fitdist,
makedist,
gpcdf,
gpinv,
gppdf,
gprnd,
gpfit,
gplike,
gpstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Generalized Pareto probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.GeneralizedParetoDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.GeneralizedParetoDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
prob.GeneralizedParetoDistribution.GeneralizedParetoDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 452
prob.GeneralizedParetoDistribution: pd = GeneralizedParetoDistribution ( k , sigma , theta )
prob.GeneralizedParetoDistribution: pd = GeneralizedParetoDistribution ()

Create a prob.GeneralizedParetoDistribution object.

k , sigma and theta are the distribution parameters,
which the class help describes. Called with no arguments the parameters
take their defaults, k 1, sigma 1 and theta 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Create a prob.GeneralizedParetoDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedParetoDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 750
prob.GeneralizedParetoDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.GeneralizedParetoDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 220
prob.GeneralizedParetoDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.GeneralizedParetoDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.GeneralizedParetoDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.GeneralizedParetoDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 632
prob.GeneralizedParetoDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 3&times;3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
prob.GeneralizedParetoDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 243
prob.GeneralizedParetoDistribution: property ParameterDescription

Description of parameters

A 3&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.GeneralizedParetoDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 299
prob.GeneralizedParetoDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.GeneralizedParetoDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 220
prob.GeneralizedParetoDistribution: property ParameterNames

Names of parameters

A 3&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.GeneralizedParetoDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 309
prob.GeneralizedParetoDistribution: property ParameterValues

Distribution parameter values

A 3&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the k , sigma , and
theta properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedParetoDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 363
prob.GeneralizedParetoDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 425
prob.GeneralizedParetoDistribution: p = cdf ( pd , x )
prob.GeneralizedParetoDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GeneralizedParetoDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 261
prob.GeneralizedParetoDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.GeneralizedParetoDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.GeneralizedParetoDistribution.k


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.GeneralizedParetoDistribution: property k

Shape parameter

A scalar value characterizing the shape of the Generalized Pareto
distribution. You can access the k property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GeneralizedParetoDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 180
prob.GeneralizedParetoDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.GeneralizedParetoDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.GeneralizedParetoDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedParetoDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.GeneralizedParetoDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GeneralizedParetoDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1010
prob.GeneralizedParetoDistribution: ci = paramci ( pd )
prob.GeneralizedParetoDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 221
prob.GeneralizedParetoDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GeneralizedParetoDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1575
prob.GeneralizedParetoDistribution: plot ( pd )
prob.GeneralizedParetoDistribution: plot ( pd , Name , Value )
prob.GeneralizedParetoDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GeneralizedParetoDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2242
prob.GeneralizedParetoDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.GeneralizedParetoDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.GeneralizedParetoDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.GeneralizedParetoDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.GeneralizedParetoDistribution: [ nlogL , param ] = proflik ( pd )
prob.GeneralizedParetoDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Generalized Pareto distribution, pnum = 1 selects
the parameter k , pnum = 2 selects the parameter
sigma , and pnum = 3 selects the parameter
theta .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.GeneralizedParetoDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 749
prob.GeneralizedParetoDistribution: r = random ( pd )
prob.GeneralizedParetoDistribution: r = random ( pd , rows )
prob.GeneralizedParetoDistribution: r = random ( pd , rows , cols , &hellip;)
prob.GeneralizedParetoDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GeneralizedParetoDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.GeneralizedParetoDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the Generalized
Pareto distribution. You can access the sigma property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.GeneralizedParetoDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GeneralizedParetoDistribution.theta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 215
prob.GeneralizedParetoDistribution: property theta

Location parameter

A scalar value characterizing the location of the Generalized Pareto
distribution. You can access the theta property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.GeneralizedParetoDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 556
prob.GeneralizedParetoDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 186
prob.GeneralizedParetoDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.HalfNormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1340
statistics: prob.HalfNormalDistribution

Half-normal probability distribution object.

A prob.HalfNormalDistribution object consists of parameters, a model
description, and sample data for a half-normal probability distribution.

The half-normal distribution is a continuous probability distribution that
models the time to failure of materials subjected to cyclic loading. It is
defined by location parameter mu and scale parameter sigma .

There are several ways to create a prob.HalfNormalDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.HalfNormalDistribution ( mu ,
sigma ) to create a half-normal distribution with fixed parameter
values mu and sigma .
Use the static method prob.HalfNormalDistribution.fit ( x ,
mu , freq ) to fit a distribution to the data in x using
the same input arguments as the hnfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the half-normal distribution can be found at
https://en.wikipedia.org/wiki/Half-normal_distribution

See also:
fitdist,
makedist,
hncdf,
hninv,
hnpdf,
hnrnd,
hnfit,
hnlike,
hnstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Half-normal probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.HalfNormalDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.HalfNormalDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.HalfNormalDistribution.HalfNormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 395
prob.HalfNormalDistribution: pd = HalfNormalDistribution ( mu , sigma )
prob.HalfNormalDistribution: pd = HalfNormalDistribution ()

Create a prob.HalfNormalDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Create a prob.HalfNormalDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.HalfNormalDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 743
prob.HalfNormalDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.HalfNormalDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.HalfNormalDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.HalfNormalDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.HalfNormalDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.HalfNormalDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 625
prob.HalfNormalDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.HalfNormalDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 236
prob.HalfNormalDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.HalfNormalDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 292
prob.HalfNormalDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.HalfNormalDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.HalfNormalDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.HalfNormalDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 293
prob.HalfNormalDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.HalfNormalDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 356
prob.HalfNormalDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.HalfNormalDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 411
prob.HalfNormalDistribution: p = cdf ( pd , x )
prob.HalfNormalDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.HalfNormalDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 254
prob.HalfNormalDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.HalfNormalDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.HalfNormalDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.HalfNormalDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.HalfNormalDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.HalfNormalDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 181
prob.HalfNormalDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.HalfNormalDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.HalfNormalDistribution: property mu

Location parameter

A scalar value characterizing the location of the
half-normal distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.HalfNormalDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 227
prob.HalfNormalDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.HalfNormalDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 996
prob.HalfNormalDistribution: ci = paramci ( pd )
prob.HalfNormalDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.HalfNormalDistribution.pdf


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prob.HalfNormalDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


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Compute the probability distribution function (PDF).



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prob.HalfNormalDistribution.plot


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prob.HalfNormalDistribution: plot ( pd )
prob.HalfNormalDistribution: plot ( pd , Name , Value )
prob.HalfNormalDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


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Plot a probability distribution object.



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prob.HalfNormalDistribution.proflik


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prob.HalfNormalDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.HalfNormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.HalfNormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.HalfNormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.HalfNormalDistribution: [ nlogL , param ] = proflik ( pd )
prob.HalfNormalDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Half-normal distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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prob.HalfNormalDistribution.random


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prob.HalfNormalDistribution: r = random ( pd )
prob.HalfNormalDistribution: r = random ( pd , rows )
prob.HalfNormalDistribution: r = random ( pd , rows , cols , &hellip;)
prob.HalfNormalDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, hnrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


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Generate random arrays from the probability distribution object.



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prob.HalfNormalDistribution.sigma


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prob.HalfNormalDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the
half-normal distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
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Scale parameter



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# length: 31
prob.HalfNormalDistribution.std


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prob.HalfNormalDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


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Compute the standard deviation of a probability distribution.



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prob.HalfNormalDistribution.truncate


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prob.HalfNormalDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


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Truncate a probability distribution.



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prob.HalfNormalDistribution.var


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prob.HalfNormalDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


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Compute the variance of a probability distribution.



# name: <cell-element>
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prob.InverseGaussianDistribution


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statistics: prob.InverseGaussianDistribution

Inverse Gaussian probability distribution object.

A prob.InverseGaussianDistribution object consists of parameters, a
model description, and sample data for a Inverse Gaussian probability
distribution.

The Inverse Gaussian distribution is a continuous probability distribution,
which is often used to model non-negative positively skewed data. Is is
defined by mean parameter mu and shape parameter lambda .

There are several ways to create a prob.InverseGaussianDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.InverseGaussianDistribution ( mu ,
lambda ) to create a Inverse Gaussian distribution with fixed
parameter values mu and lambda .
Use the static method prob.InverseGaussianDistribution.fit
( x , alpha , censor , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
invgfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Inverse Gaussian distribution can be found at
https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution

See also:
fitdist,
makedist,
invgcdf,
invginv,
invgpdf,
invgrnd,
invgfit,
invglike,
invgstat


# name: <cell-element>
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Inverse Gaussian probability distribution object.



# name: <cell-element>
# type: sq_string
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prob.InverseGaussianDistribution.DistributionName


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# type: sq_string
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prob.InverseGaussianDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
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Probability distribution name



# name: <cell-element>
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prob.InverseGaussianDistribution.InputData


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prob.InverseGaussianDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
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Data used for fitting a probability distribution



# name: <cell-element>
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# length: 60
prob.InverseGaussianDistribution.InverseGaussianDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 423
prob.InverseGaussianDistribution: pd = InverseGaussianDistribution ( mu , lambda )
prob.InverseGaussianDistribution: pd = InverseGaussianDistribution ()

Create a prob.InverseGaussianDistribution object.

mu and lambda are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, mu 1 and lambda 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
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Create a prob.InverseGaussianDistribution object.



# name: <cell-element>
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prob.InverseGaussianDistribution.IsTruncated


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# type: sq_string
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prob.InverseGaussianDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
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Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.InverseGaussianDistribution.NumParameters


# name: <cell-element>
# type: sq_string
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# length: 211
prob.InverseGaussianDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
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Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.InverseGaussianDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 630
prob.InverseGaussianDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
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Covariance matrix of the parameter estimates



# name: <cell-element>
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prob.InverseGaussianDistribution.ParameterDescription


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prob.InverseGaussianDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.InverseGaussianDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
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# length: 297
prob.InverseGaussianDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
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# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.InverseGaussianDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.InverseGaussianDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.InverseGaussianDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 299
prob.InverseGaussianDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and lambda
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.InverseGaussianDistribution.Truncation


# name: <cell-element>
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# length: 361
prob.InverseGaussianDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.cdf


# name: <cell-element>
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# length: 421
prob.InverseGaussianDistribution: p = cdf ( pd , x )
prob.InverseGaussianDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



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prob.InverseGaussianDistribution.icdf


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prob.InverseGaussianDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


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Compute the inverse cumulative distribution function (iCDF).



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prob.InverseGaussianDistribution.iqr


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prob.InverseGaussianDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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Compute the interquartile range of a probability distribution.



# name: <cell-element>
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# length: 39
prob.InverseGaussianDistribution.lambda


# name: <cell-element>
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# length: 216
prob.InverseGaussianDistribution: property lambda

Shape parameter

A positive scalar value characterizing the shape of the
Inverse Gaussian distribution. You can access the lambda
property using dot name assignment.


# name: <cell-element>
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# length: 15
Shape parameter



# name: <cell-element>
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# length: 37
prob.InverseGaussianDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 178
prob.InverseGaussianDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.InverseGaussianDistribution.median


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prob.InverseGaussianDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


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Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
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# length: 35
prob.InverseGaussianDistribution.mu


# name: <cell-element>
# type: sq_string
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prob.InverseGaussianDistribution: property mu

Mean parameter

A positive scalar value characterizing the mean of the
Inverse Gaussian distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
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# length: 14
Mean parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.InverseGaussianDistribution.negloglik


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# elements: 1
# length: 232
prob.InverseGaussianDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


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Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.InverseGaussianDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1006
prob.InverseGaussianDistribution: ci = paramci ( pd )
prob.InverseGaussianDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.InverseGaussianDistribution.pdf


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# type: sq_string
# elements: 1
# length: 219
prob.InverseGaussianDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


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Compute the probability distribution function (PDF).



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prob.InverseGaussianDistribution.plot


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prob.InverseGaussianDistribution: plot ( pd )
prob.InverseGaussianDistribution: plot ( pd , Name , Value )
prob.InverseGaussianDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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Plot a probability distribution object.



# name: <cell-element>
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prob.InverseGaussianDistribution.proflik


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prob.InverseGaussianDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.InverseGaussianDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.InverseGaussianDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.InverseGaussianDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.InverseGaussianDistribution: [ nlogL , param ] = proflik ( pd )
prob.InverseGaussianDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Inverse Gaussian distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter lambda .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.InverseGaussianDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 742
prob.InverseGaussianDistribution: r = random ( pd )
prob.InverseGaussianDistribution: r = random ( pd , rows )
prob.InverseGaussianDistribution: r = random ( pd , rows , cols , &hellip;)
prob.InverseGaussianDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, invgrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.InverseGaussianDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.InverseGaussianDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 554
prob.InverseGaussianDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 184
prob.InverseGaussianDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.KernelDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 840
statistics: prob.KernelDistribution

Kernel probability distribution object.

A prob.KernelDistribution object consists of a nonparametric kernel
smoothing density estimate fitted to sample data, together with a model
description. Unlike the parametric distribution objects, it has no
estimated parameters; the fitted distribution is defined entirely by the
data, the smoothing kernel, and the bandwidth.

A prob.KernelDistribution object can only be created by fitting a kernel
smoothing distribution to data with the fitdist function. Unlike
the parametric distributions, it cannot be created with the makedist
function, since it is not parametric and requires data.

Further information about the kernel density estimation can be found at
https://en.wikipedia.org/wiki/Kernel_density_estimation

See also:
fitdist,
ksdensity,
mvksdensity


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Kernel probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.KernelDistribution.Bandwidth


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.KernelDistribution: property Bandwidth

Bandwidth of the smoothing kernel

A positive scalar value specifying the bandwidth of the smoothing kernel.
You can access the Bandwidth property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
Bandwidth of the smoothing kernel



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.KernelDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.KernelDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.KernelDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 572
prob.KernelDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : an empty array, since censoring is not supported for
a kernel distribution.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.KernelDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.KernelDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.KernelDistribution.Kernel


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 285
prob.KernelDistribution: property Kernel

Kernel smoothing function

A character vector specifying the type of smoothing kernel used for the
density estimate. It is one of 'normal' , 'box' ,
'triangle' , or 'epanechnikov' . You can access the
Kernel property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Kernel smoothing function



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.KernelDistribution.KernelDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 479
prob.KernelDistribution: pd = KernelDistribution ( data , kernel , bw , support , freq )
prob.KernelDistribution: pd = KernelDistribution ()

Create a prob.KernelDistribution object.

data , kernel , bw , support and freq are the
distribution parameters, which the class help describes. Called with no
arguments it fits the data [0; 1] with a normal kernel over an
unbounded support, taking the bandwidth from the data.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Create a prob.KernelDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.KernelDistribution.Support


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 472
prob.KernelDistribution: property Support

Support of the probability distribution

A scalar structure containing the following fields:

range : either the character vector 'unbounded' or
'positive' , or a two-element numeric vector [L, U] with the
lower and upper bounds of the support.
closedbound : a two-element logical vector specifying whether
each bound is closed.
iscontinuous : a logical scalar, always true for a
kernel distribution.

This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Support of the probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.KernelDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 352
prob.KernelDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 486
prob.KernelDistribution: p = cdf ( pd , x )
prob.KernelDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .

x must be double or single ; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.KernelDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 333
prob.KernelDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .

p must be double or single ; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.KernelDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.KernelDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 169
prob.KernelDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.KernelDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.KernelDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.KernelDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 223
prob.KernelDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 288
prob.KernelDistribution: y = pdf ( pd , x )

Compute the probability density function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .

x must be double or single ; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the probability density function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.KernelDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1032
prob.KernelDistribution: plot ( pd )
prob.KernelDistribution: plot ( pd , Name , Value )
prob.KernelDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd , superimposed over a histogram
of the data used to fit it.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF)
superimposed on a histogram of the data. 'cdf' plots the
cumulative distribution function (CDF) superimposed over an empirical
CDF. 'probability' plots a probability plot using a CDF of the
data and a CDF of the fitted probability distribution.
'Parent' An axes graphics object for plot. If not
specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.KernelDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 705
prob.KernelDistribution: r = random ( pd )
prob.KernelDistribution: r = random ( pd , rows )
prob.KernelDistribution: r = random ( pd , rows , cols , &hellip;)
prob.KernelDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.KernelDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.KernelDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 302
prob.KernelDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.KernelDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.LogisticDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1356
statistics: prob.LogisticDistribution

Logistic probability distribution object.

A prob.LogisticDistribution object consists of parameters, a model
description, and sample data for a logistic probability distribution.

The logistic distribution is a continuous probability distribution, which
is commonly used in logistic regression and feedforward neural networks.
It is defined by location parameter mu and scale parameter
sigma .

There are several ways to create a prob.LogisticDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.LogisticDistribution ( mu ,
sigma ) to create a logistic distribution with fixed parameter values
mu and sigma .
Use the static method prob.LogisticDistribution.fit ( x ,
alpha , censor , freq , options ) to fit a
distribution to the data in x using the same input arguments as the
logifit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the logistic distribution can be found at
https://en.wikipedia.org/wiki/Logistic_distribution

See also:
fitdist,
makedist,
logicdf,
logiinv,
logipdf,
logirnd,
logifit,
logilike,
logistat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Logistic probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LogisticDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.LogisticDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.LogisticDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 741
prob.LogisticDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.LogisticDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.LogisticDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.LogisticDistribution.LogisticDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 385
prob.LogisticDistribution: pd = LogisticDistribution ( mu , sigma )
prob.LogisticDistribution: pd = LogisticDistribution ()

Create a prob.LogisticDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
Create a prob.LogisticDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.LogisticDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.LogisticDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.LogisticDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 623
prob.LogisticDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.LogisticDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.LogisticDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LogisticDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 290
prob.LogisticDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.LogisticDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.LogisticDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.LogisticDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 291
prob.LogisticDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LogisticDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 354
prob.LogisticDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LogisticDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 407
prob.LogisticDistribution: p = cdf ( pd , x )
prob.LogisticDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LogisticDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 252
prob.LogisticDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LogisticDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.LogisticDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
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prob.LogisticDistribution.mean


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# type: sq_string
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prob.LogisticDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
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Compute the mean of a probability distribution.



# name: <cell-element>
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prob.LogisticDistribution.median


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# type: sq_string
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prob.LogisticDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
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Compute the median of a probability distribution.



# name: <cell-element>
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prob.LogisticDistribution.mu


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prob.LogisticDistribution: property mu

Location parameter

A scalar value characterizing the location of the
logistic distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
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Location parameter



# name: <cell-element>
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# length: 35
prob.LogisticDistribution.negloglik


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prob.LogisticDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
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Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
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prob.LogisticDistribution.paramci


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prob.LogisticDistribution: ci = paramci ( pd )
prob.LogisticDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


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Compute the confidence intervals for probability distribution parameters.



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# length: 29
prob.LogisticDistribution.pdf


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prob.LogisticDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


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Compute the probability distribution function (PDF).



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prob.LogisticDistribution.plot


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prob.LogisticDistribution: plot ( pd )
prob.LogisticDistribution: plot ( pd , Name , Value )
prob.LogisticDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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Plot a probability distribution object.



# name: <cell-element>
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prob.LogisticDistribution.proflik


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prob.LogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.LogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.LogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.LogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.LogisticDistribution: [ nlogL , param ] = proflik ( pd )
prob.LogisticDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the logistic distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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prob.LogisticDistribution.random


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prob.LogisticDistribution: r = random ( pd )
prob.LogisticDistribution: r = random ( pd , rows )
prob.LogisticDistribution: r = random ( pd , rows , cols , &hellip;)
prob.LogisticDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, bisarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
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Generate random arrays from the probability distribution object.



# name: <cell-element>
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prob.LogisticDistribution.sigma


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prob.LogisticDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the
logistic distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
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Scale parameter



# name: <cell-element>
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# elements: 1
# length: 29
prob.LogisticDistribution.std


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# length: 197
prob.LogisticDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


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Compute the standard deviation of a probability distribution.



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prob.LogisticDistribution.truncate


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prob.LogisticDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower ,
and upper limit, upper . If pd is fitted to data with
fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


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Truncate a probability distribution.



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prob.LogisticDistribution.var


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prob.LogisticDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


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Compute the variance of a probability distribution.



# name: <cell-element>
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prob.LoglogisticDistribution


# name: <cell-element>
# type: sq_string
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# length: 1400
statistics: prob.LoglogisticDistribution

Log-logistic probability distribution object.

A prob.LoglogisticDistribution object consists of parameters, a model
description, and sample data for a log-logistic probability distribution.

The log-logistic distribution is a continuous probability distribution that
models non-negative random variables whose logarithm follows the logistic
distribution. It is defined by location parameter mu and scale
parameter sigma .

There are several ways to create a prob.LoglogisticDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.LoglogisticDistribution ( mu ,
sigma ) to create a log-logistic distribution with fixed parameter
values mu and sigma .
Use the static method prob.LoglogisticDistribution.fit ( x ,
censor , freq , options ) to fit a distribution to the data
in x using the same input arguments as the loglfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the log-logistic distribution can be found at
https://en.wikipedia.org/wiki/Log-logistic_distribution

See also:
fitdist,
makedist,
loglcdf,
loglinv,
loglpdf,
loglrnd,
loglfit,
logllike,
loglstat


# name: <cell-element>
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Log-logistic probability distribution object.



# name: <cell-element>
# type: sq_string
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prob.LoglogisticDistribution.DistributionName


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# type: sq_string
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prob.LoglogisticDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
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Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LoglogisticDistribution.InputData


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# type: sq_string
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prob.LoglogisticDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
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Data used for fitting a probability distribution



# name: <cell-element>
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# length: 40
prob.LoglogisticDistribution.IsTruncated


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prob.LoglogisticDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


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Flag for truncated probability distribution



# name: <cell-element>
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# elements: 1
# length: 52
prob.LoglogisticDistribution.LoglogisticDistribution


# name: <cell-element>
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# length: 400
prob.LoglogisticDistribution: pd = LoglogisticDistribution ( mu , sigma )
prob.LoglogisticDistribution: pd = LoglogisticDistribution ()

Create a prob.LoglogisticDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
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Create a prob.LoglogisticDistribution object.



# name: <cell-element>
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prob.LoglogisticDistribution.NumParameters


# name: <cell-element>
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prob.LoglogisticDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
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Number of parameters



# name: <cell-element>
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prob.LoglogisticDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
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# length: 626
prob.LoglogisticDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
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Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
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# length: 49
prob.LoglogisticDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 237
prob.LoglogisticDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
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# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.LoglogisticDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 293
prob.LoglogisticDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LoglogisticDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.LoglogisticDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.LoglogisticDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.LoglogisticDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
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# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.LoglogisticDistribution.Truncation


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prob.LoglogisticDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
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Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.cdf


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prob.LoglogisticDistribution: p = cdf ( pd , x )
prob.LoglogisticDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



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prob.LoglogisticDistribution.icdf


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prob.LoglogisticDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


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Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.iqr


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# type: sq_string
# elements: 1
# length: 202
prob.LoglogisticDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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# type: sq_string
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# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
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# elements: 1
# length: 33
prob.LoglogisticDistribution.mean


# name: <cell-element>
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# elements: 1
# length: 174
prob.LoglogisticDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
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# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.LoglogisticDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 182
prob.LoglogisticDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoglogisticDistribution.mu


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prob.LoglogisticDistribution: property mu

Mean of logarithmic values

A scalar value characterizing the mean of the logarithmic values of the
log-logistic distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
Mean of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LoglogisticDistribution.negloglik


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prob.LoglogisticDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


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Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
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# length: 36
prob.LoglogisticDistribution.paramci


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prob.LoglogisticDistribution: ci = paramci ( pd )
prob.LoglogisticDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.LoglogisticDistribution.pdf


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prob.LoglogisticDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


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Compute the probability distribution function (PDF).



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prob.LoglogisticDistribution.plot


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prob.LoglogisticDistribution: plot ( pd )
prob.LoglogisticDistribution: plot ( pd , Name , Value )
prob.LoglogisticDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
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Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
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prob.LoglogisticDistribution.proflik


# name: <cell-element>
# type: sq_string
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# length: 2160
prob.LoglogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.LoglogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.LoglogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.LoglogisticDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.LoglogisticDistribution: [ nlogL , param ] = proflik ( pd )
prob.LoglogisticDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Log-logistic distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
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Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
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# length: 35
prob.LoglogisticDistribution.random


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# type: sq_string
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# length: 725
prob.LoglogisticDistribution: r = random ( pd )
prob.LoglogisticDistribution: r = random ( pd , rows )
prob.LoglogisticDistribution: r = random ( pd , rows , cols , &hellip;)
prob.LoglogisticDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
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Generate random arrays from the probability distribution object.



# name: <cell-element>
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# length: 34
prob.LoglogisticDistribution.sigma


# name: <cell-element>
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# length: 244
prob.LoglogisticDistribution: property sigma

Scale of logarithmic values

A positive scalar value characterizing the scale of the logarithmic
values of the log-logistic distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
Scale of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.std


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# type: sq_string
# elements: 1
# length: 200
prob.LoglogisticDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
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Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.LoglogisticDistribution.truncate


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# length: 550
prob.LoglogisticDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
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Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.var


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prob.LoglogisticDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
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# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.LognormalDistribution


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# type: sq_string
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# length: 1355
statistics: prob.LognormalDistribution

Lognormal probability distribution object.

A prob.LognormalDistribution object consists of parameters, a model
description, and sample data for a lognormal probability distribution.

The lognormal distribution is a continuous probability distribution whose
logarithm is normally distributed. It is defined by mean parameter
mu and standard deviation parameter sigma of the logarithmic
values.

There are several ways to create a prob.LognormalDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.LognormalDistribution ( mu ,
sigma ) to create a lognormal distribution with fixed parameter
values mu and sigma .
Use the static method prob.LognormalDistribution.fit ( x ,
censor , freq , options ) to fit a distribution to the
data in x using the same input arguments as the lognfit
function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the lognormal distribution can be found at
https://en.wikipedia.org/wiki/Log-normal_distribution

See also:
fitdist,
makedist,
logncdf,
logninv,
lognpdf,
lognrnd,
lognfit,
lognlike,
lognstat


# name: <cell-element>
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Lognormal probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LognormalDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.LognormalDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LognormalDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 742
prob.LognormalDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
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# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LognormalDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
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# length: 212
prob.LognormalDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
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# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.LognormalDistribution.LognormalDistribution


# name: <cell-element>
# type: sq_string
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# length: 390
prob.LognormalDistribution: pd = LognormalDistribution ( mu , sigma )
prob.LognormalDistribution: pd = LognormalDistribution ()

Create a prob.LognormalDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
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# length: 43
Create a prob.LognormalDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.LognormalDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.LognormalDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
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# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.LognormalDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 624
prob.LognormalDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.LognormalDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 235
prob.LognormalDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LognormalDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 291
prob.LognormalDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.LognormalDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.LognormalDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LognormalDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 292
prob.LognormalDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.LognormalDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 355
prob.LognormalDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.cdf


# name: <cell-element>
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# length: 409
prob.LognormalDistribution: p = cdf ( pd , x )
prob.LognormalDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



# name: <cell-element>
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# length: 31
prob.LognormalDistribution.icdf


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prob.LognormalDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.iqr


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# length: 200
prob.LognormalDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LognormalDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.LognormalDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
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# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LognormalDistribution.median


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# type: sq_string
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# length: 180
prob.LognormalDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
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# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LognormalDistribution.mu


# name: <cell-element>
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# elements: 1
# length: 222
prob.LognormalDistribution: property mu

Mean of logarithmic values

A scalar value characterizing the mean of the logarithmic values of the
lognormal distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
Mean of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LognormalDistribution.negloglik


# name: <cell-element>
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# length: 226
prob.LognormalDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
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# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LognormalDistribution.paramci


# name: <cell-element>
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# length: 994
prob.LognormalDistribution: ci = paramci ( pd )
prob.LognormalDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
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Compute the confidence intervals for probability distribution parameters.



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# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.pdf


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# length: 213
prob.LognormalDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
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# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LognormalDistribution.plot


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# length: 1551
prob.LognormalDistribution: plot ( pd )
prob.LognormalDistribution: plot ( pd , Name , Value )
prob.LognormalDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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Plot a probability distribution object.



# name: <cell-element>
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# elements: 1
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prob.LognormalDistribution.proflik


# name: <cell-element>
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# length: 2145
prob.LognormalDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.LognormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.LognormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.LognormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.LognormalDistribution: [ nlogL , param ] = proflik ( pd )
prob.LognormalDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Lognormal distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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prob.LognormalDistribution.random


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prob.LognormalDistribution: r = random ( pd )
prob.LognormalDistribution: r = random ( pd , rows )
prob.LognormalDistribution: r = random ( pd , rows , cols , &hellip;)
prob.LognormalDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, lognrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
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# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LognormalDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 265
prob.LognormalDistribution: property sigma

Standard deviation of logarithmic values

A positive scalar value characterizing the standard deviation of the
logarithmic values of the lognormal distribution. You can access the
sigma property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Standard deviation of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.LognormalDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


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Compute the standard deviation of a probability distribution.



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prob.LognormalDistribution.truncate


# name: <cell-element>
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prob.LognormalDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 178
prob.LognormalDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.LoguniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 944
statistics: prob.LoguniformDistribution

Log-uniform probability distribution object.

A prob.LoguniformDistribution object consists of parameters and a model
description for a log-uniform probability distribution.

The log-uniform distribution is a continuous probability distribution that
is constant between locations Lower and Upper on a logarithmic
scale.

There are several ways to create a prob.LoguniformDistribution object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor prob.LoguniformDistribution ( Lower ,
Upper ) to create a log-uniform distribution with specified parameter
values Lower and Upper .

It is highly recommended to use makedist function to create
probability distribution objects, instead of the class constructor.

Further information about the log-uniform distribution can be found at
https://en.wikipedia.org/wiki/Reciprocal_distribution

See also:
makedist


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Log-uniform probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.LoguniformDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.LoguniformDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.LoguniformDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.LoguniformDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.LoguniformDistribution.LoguniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 404
prob.LoguniformDistribution: pd = LoguniformDistribution ( Lower , Upper )
prob.LoguniformDistribution: pd = LoguniformDistribution ()

Create a prob.LoguniformDistribution object.

Lower and Upper are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, Lower 1 and Upper 4.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Create a prob.LoguniformDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LoguniformDistribution.Lower


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.LoguniformDistribution: property Lower

Lower limit

A positive scalar value characterizing the lower limit of the
log-uniform distribution. You can access the Lower
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
Lower limit



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.LoguniformDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.LoguniformDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.LoguniformDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 236
prob.LoguniformDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LoguniformDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.LoguniformDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LoguniformDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 296
prob.LoguniformDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the Lower and Upper
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LoguniformDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 356
prob.LoguniformDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LoguniformDistribution.Upper


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.LoguniformDistribution: property Upper

Upper limit

A positive scalar value characterizing the upper limit of the
log-uniform distribution. You can access the Upper
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
Upper limit



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 494
prob.LoguniformDistribution: p = cdf ( pd , x )
prob.LoguniformDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .

x must be double or single ; integer, logical,
and character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoguniformDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 337
prob.LoguniformDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .

p must be double or single ; integer, logical,
and character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.LoguniformDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoguniformDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.LoguniformDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LoguniformDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 181
prob.LoguniformDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 297
prob.LoguniformDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .

x must be double or single ; integer, logical,
and character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoguniformDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1126
prob.LoguniformDistribution: plot ( pd )
prob.LoguniformDistribution: plot ( pd , Name , Value )
prob.LoguniformDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd .

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF).
'cdf' plots the cumulative density function (CDF).
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LoguniformDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 721
prob.LoguniformDistribution: r = random ( pd )
prob.LoguniformDistribution: r = random ( pd , rows )
prob.LoguniformDistribution: r = random ( pd , rows , cols , &hellip;)
prob.LoguniformDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.LoguniformDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LoguniformDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 306
prob.LoguniformDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.LoguniformDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.MultinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1083
statistics: prob.MultinomialDistribution

Multinomial probability distribution object.

A prob.MultinomialDistribution object consists of parameters, a model
description, and sample data for a multinomial probability distribution.

The multinomial distribution is a discrete probability distribution that
models the outcomes of n independent trials of a k-category system, where
each trial has a probability of falling into each category. It is
defined by the vector of probabilities for each outcome.

There are several ways to create a prob.MultinomialDistribution object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor
prob.MultinomialDistribution
( Probabilities )
to create a multinomial distribution with specified parameter values.

It is highly recommended to use the makedist function to create
probability distribution objects, instead of the constructor.

Further information about the multinomial distribution can be found at
https://en.wikipedia.org/wiki/Multinomial_distribution

See also:
makedist,
mnpdf,
mnrnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Multinomial probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.MultinomialDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.MultinomialDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.MultinomialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.MultinomialDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.MultinomialDistribution.MultinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 408
prob.MultinomialDistribution: pd = MultinomialDistribution ( Probabilities )
prob.MultinomialDistribution: pd = MultinomialDistribution ()

Create a prob.MultinomialDistribution object.

Probabilities is the distribution parameter, which the class help
describes. Called with no arguments the parameter takes its default,
Probabilities [0.5, 0.5] .

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
Create a prob.MultinomialDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.MultinomialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.MultinomialDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.MultinomialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 237
prob.MultinomialDistribution: property ParameterDescription

Description of parameters

A 1&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.MultinomialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.MultinomialDistribution: property ParameterNames

Names of parameters

A 1&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.MultinomialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 283
prob.MultinomialDistribution: property ParameterValues

Distribution parameter values

A numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the Probabilities
property.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.MultinomialDistribution.Probabilities


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.MultinomialDistribution: property Probabilities

Outcome probabilities

A row vector of probabilities for each outcome. You can access the
Probabilities property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Outcome probabilities



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.MultinomialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 357
prob.MultinomialDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 582
prob.MultinomialDistribution: p = cdf ( pd , x )
prob.MultinomialDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .

x must be double , single , or an integer type;
logical and character arrays are rejected. Integer input is promoted
to double , so the result is always a probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.MultinomialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 338
prob.MultinomialDistribution: p = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

p = icdf ( pd , x ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in x .

p must be double or single ; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.MultinomialDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.MultinomialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 174
prob.MultinomialDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.MultinomialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 182
prob.MultinomialDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 384
prob.MultinomialDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .

x must be double , single , or an integer type;
logical and character arrays are rejected. Integer input is promoted
to double , so the result is always a probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.MultinomialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1555
prob.MultinomialDistribution: plot ( pd )
prob.MultinomialDistribution: plot ( pd , Name , Value )
prob.MultinomialDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.MultinomialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 724
prob.MultinomialDistribution: y = random ( pd )
prob.MultinomialDistribution: y = random ( pd , rows )
prob.MultinomialDistribution: y = random ( pd , rows , cols , &hellip;)
prob.MultinomialDistribution: y = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, mnrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.MultinomialDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.MultinomialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 534
prob.MultinomialDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd ) returns a probability distribution
t , which is the probability distribution pd truncated to the
specified interval with lower limit, lower , and upper limit,
upper . If pd is fitted to data with fitdist , the
returned probability distribution t is not fitted, does not contain
any data or estimated values, and it is as it has been created with the
makedist function, but it includes the truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.MultinomialDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.NakagamiDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1353
statistics: prob.NakagamiDistribution

Nakagami probability distribution object.

A prob.NakagamiDistribution object consists of parameters, a model
description, and sample data for a Nakagami probability distribution.

The Nakagami distribution is a continuous probability distribution that
models the amplitude of received signals after maximum ratio diversity
combining. It is defined by shape parameter mu and spread parameter
omega .

There are several ways to create a prob.NakagamiDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.NakagamiDistribution ( mu ,
omega ) to create a Nakagami distribution with fixed parameter
values mu and omega .
Use the static method prob.NakagamiDistribution.fit ( x ,
censor , freq , options ) to fit a distribution to the data
in x using the same input arguments as the nakafit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Nakagami distribution can be found at
https://en.wikipedia.org/wiki/Nakagami_distribution

See also:
fitdist,
makedist,
nakacdf,
nakainv,
nakapdf,
nakarnd,
nakafit,
nakalike,
nakastat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Nakagami probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NakagamiDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.NakagamiDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NakagamiDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 741
prob.NakagamiDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NakagamiDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.NakagamiDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.NakagamiDistribution.NakagamiDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 385
prob.NakagamiDistribution: pd = NakagamiDistribution ( mu , omega )
prob.NakagamiDistribution: pd = NakagamiDistribution ()

Create a prob.NakagamiDistribution object.

mu and omega are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 1 and omega 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
Create a prob.NakagamiDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.NakagamiDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.NakagamiDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.NakagamiDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 623
prob.NakagamiDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.NakagamiDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.NakagamiDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NakagamiDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 290
prob.NakagamiDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NakagamiDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.NakagamiDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.NakagamiDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 291
prob.NakagamiDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and omega
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.NakagamiDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 354
prob.NakagamiDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 407
prob.NakagamiDistribution: p = cdf ( pd , x )
prob.NakagamiDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.NakagamiDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 252
prob.NakagamiDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.NakagamiDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.NakagamiDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.NakagamiDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.NakagamiDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.NakagamiDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.NakagamiDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.NakagamiDistribution: property mu

Shape parameter

A positive scalar value characterizing the shape of the
Nakagami distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NakagamiDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.NakagamiDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.NakagamiDistribution.omega


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.NakagamiDistribution: property omega

Spread parameter

A positive scalar value characterizing the spread of the
Nakagami distribution. You can access the omega
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
Spread parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NakagamiDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 992
prob.NakagamiDistribution: ci = paramci ( pd )
prob.NakagamiDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.NakagamiDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.NakagamiDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1548
prob.NakagamiDistribution: plot ( pd )
prob.NakagamiDistribution: plot ( pd , Name , Value )
prob.NakagamiDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NakagamiDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2138
prob.NakagamiDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.NakagamiDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.NakagamiDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.NakagamiDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.NakagamiDistribution: [ nlogL , param ] = proflik ( pd )
prob.NakagamiDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Nakagami distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter omega .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.NakagamiDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 714
prob.NakagamiDistribution: r = random ( pd )
prob.NakagamiDistribution: r = random ( pd , rows )
prob.NakagamiDistribution: r = random ( pd , rows , cols , &hellip;)
prob.NakagamiDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.NakagamiDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.NakagamiDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 547
prob.NakagamiDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.NakagamiDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NegativeBinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1521
statistics: prob.NegativeBinomialDistribution

Negative binomial probability distribution object.

A prob.NegativeBinomialDistribution object consists of parameters, a
model description, and sample data for a negative binomial probability
distribution.

The negative binomial distribution is a discrete probability distribution
that models the number of failures in a sequence of independent and
identically distributed Bernoulli trials before a specified (non-random)
number of successes occurs. It is defined by the number of successes
R and the probability of success P .

There are several ways to create a prob.NegativeBinomialDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.NegativeBinomialDistribution ( R ,
P ) to create a negative binomial distribution with fixed parameter
values R and P .
Use the static method
prob.NegativeBinomialDistribution.fit
( x ,
freq , options ) to fit a distribution to the data in x
using the same input arguments as the nbinfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the negative binomial distribution can be found
at https://en.wikipedia.org/wiki/Negative_binomial_distribution

See also:
fitdist,
makedist,
nbincdf,
nbininv,
nbinpdf,
nbinrnd,
nbinfit,
nbinlike,
nbinstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Negative binomial probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.NegativeBinomialDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.NegativeBinomialDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.NegativeBinomialDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 749
prob.NegativeBinomialDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.NegativeBinomialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.NegativeBinomialDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
prob.NegativeBinomialDistribution.NegativeBinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 412
prob.NegativeBinomialDistribution: pd = NegativeBinomialDistribution ( R , P )
prob.NegativeBinomialDistribution: pd = NegativeBinomialDistribution ()

Create a prob.NegativeBinomialDistribution object.

R and P are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
R 1 and P 0.5.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Create a prob.NegativeBinomialDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.NegativeBinomialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.NegativeBinomialDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NegativeBinomialDistribution.P


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 223
prob.NegativeBinomialDistribution: property P

Probability of success

A scalar value characterizing the probability of success in the
negative binomial distribution. You can access the P
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
Probability of success



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
prob.NegativeBinomialDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 631
prob.NegativeBinomialDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.NegativeBinomialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 242
prob.NegativeBinomialDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.NegativeBinomialDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 298
prob.NegativeBinomialDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.NegativeBinomialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.NegativeBinomialDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.NegativeBinomialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.NegativeBinomialDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the R and P
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NegativeBinomialDistribution.R


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.NegativeBinomialDistribution: property R

Number of successes

A scalar value characterizing the number of successes in the
negative binomial distribution. You can access the R
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Number of successes



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.NegativeBinomialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 362
prob.NegativeBinomialDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 423
prob.NegativeBinomialDistribution: p = cdf ( pd , x )
prob.NegativeBinomialDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NegativeBinomialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 260
prob.NegativeBinomialDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.NegativeBinomialDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NegativeBinomialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.NegativeBinomialDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NegativeBinomialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
prob.NegativeBinomialDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.NegativeBinomialDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.NegativeBinomialDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.NegativeBinomialDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1008
prob.NegativeBinomialDistribution: ci = paramci ( pd )
prob.NegativeBinomialDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 220
prob.NegativeBinomialDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NegativeBinomialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1572
prob.NegativeBinomialDistribution: plot ( pd )
prob.NegativeBinomialDistribution: plot ( pd , Name , Value )
prob.NegativeBinomialDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.NegativeBinomialDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2190
prob.NegativeBinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.NegativeBinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.NegativeBinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.NegativeBinomialDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.NegativeBinomialDistribution: [ nlogL , param ] = proflik ( pd )
prob.NegativeBinomialDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the negative binomial distribution, pnum = 1 selects
the parameter R and pnum = 2 selects the
parameter P .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NegativeBinomialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 747
prob.NegativeBinomialDistribution: r = random ( pd )
prob.NegativeBinomialDistribution: r = random ( pd , rows )
prob.NegativeBinomialDistribution: r = random ( pd , rows , cols , &hellip;)
prob.NegativeBinomialDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, nbindrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.NegativeBinomialDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NegativeBinomialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 555
prob.NegativeBinomialDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 185
prob.NegativeBinomialDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.NormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1317
statistics: prob.NormalDistribution

Normal probability distribution object.

A prob.NormalDistribution object consists of parameters, a model
description, and sample data for a normal probability distribution.

The normal distribution is a continuous probability distribution that is
symmetric about the mean, mu , showing that data near the mean are
more frequent in occurrence than data far from the mean. It is defined by
location parameter mu and scale parameter sigma .

There are several ways to create a prob.NormalDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.NormalDistribution ( mu ,
sigma )
to create a normal distribution with fixed parameter values mu and
sigma .
Use the static method prob.NormalDistribution.fit ( x ,
censor , freq , options ) to fit a distribution to data
x .

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the normal distribution can be found at
https://en.wikipedia.org/wiki/Normal_distribution

See also:
fitdist,
makedist,
normcdf,
norminv,
normpdf,
normrnd,
normfit,
normlike,
normstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Normal probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NormalDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.NormalDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NormalDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 739
prob.NormalDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NormalDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.NormalDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NormalDistribution.NormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 375
prob.NormalDistribution: pd = NormalDistribution ( mu , sigma )
prob.NormalDistribution: pd = NormalDistribution ()

Create a prob.NormalDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Create a prob.NormalDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NormalDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.NormalDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.NormalDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 621
prob.NormalDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.NormalDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 232
prob.NormalDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NormalDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 288
prob.NormalDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NormalDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.NormalDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.NormalDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 289
prob.NormalDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.NormalDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 352
prob.NormalDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 403
prob.NormalDistribution: p = cdf ( pd , x )
prob.NormalDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
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prob.NormalDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 250
prob.NormalDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.NormalDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.NormalDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 169
prob.NormalDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.NormalDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.NormalDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.NormalDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 186
prob.NormalDistribution: property mu

Location parameter

A scalar value characterizing the location of the normal distribution.
You can access the mu property using dot name assignment.


# name: <cell-element>
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# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NormalDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 223
prob.NormalDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
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# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.NormalDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 988
prob.NormalDistribution: ci = paramci ( pd )
prob.NormalDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
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# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.pdf


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# type: sq_string
# elements: 1
# length: 210
prob.NormalDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
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Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.NormalDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1542
prob.NormalDistribution: plot ( pd )
prob.NormalDistribution: plot ( pd , Name , Value )
prob.NormalDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
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Plot a probability distribution object.



# name: <cell-element>
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prob.NormalDistribution.proflik


# name: <cell-element>
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prob.NormalDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.NormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.NormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.NormalDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.NormalDistribution: [ nlogL , param ] = proflik ( pd )
prob.NormalDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the normal distribution, pnum = 1 selects the
parameter mu and pnum = 2 selects the parameter
sigma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
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Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
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# length: 30
prob.NormalDistribution.random


# name: <cell-element>
# type: sq_string
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prob.NormalDistribution: r = random ( pd )
prob.NormalDistribution: r = random ( pd , rows )
prob.NormalDistribution: r = random ( pd , rows , cols , &hellip;)
prob.NormalDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, normrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
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Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
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# length: 29
prob.NormalDistribution.sigma


# name: <cell-element>
# type: sq_string
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prob.NormalDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the normal
distribution. You can access the sigma property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.NormalDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.NormalDistribution.truncate


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# type: sq_string
# elements: 1
# length: 545
prob.NormalDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
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# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.var


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# type: sq_string
# elements: 1
# length: 175
prob.NormalDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.PiecewiseLinearDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1184
statistics: prob.PiecewiseLinearDistribution

Piecewise linear probability distribution object.

A prob.PiecewiseLinearDistribution object consists of parameters, a model
description, and sample data for a piecewise linear probability
distribution.

The piecewise linear distribution is a continuous probability distribution
that is defined by a set of points where the cumulative distribution
function (CDF) changes slope. It is defined by a vector of x values
and a corresponding vector of CDF values Fx .

There are several ways to create a prob.PiecewiseLinearDistribution
object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor prob.PiecewiseLinearDistribution ( x ,
Fx ) to create a piecewise linear distribution with specified
parameter values x and Fx .

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the piecewise linear distribution can be found at
https://en.wikipedia.org/wiki/Piecewise_linear_function

See also:
makedist,
plcdf,
plinv,
plpdf,
plrnd,
plstat


# name: <cell-element>
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Piecewise linear probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.PiecewiseLinearDistribution.DistributionName


# name: <cell-element>
# type: sq_string
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# length: 198
prob.PiecewiseLinearDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.PiecewiseLinearDistribution.Fx


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 244
prob.PiecewiseLinearDistribution: property Fx

Vector of CDF values

A numeric row vector of CDF values that correspond to each value in
x , reported as a row whichever way it was given. You can access
the Fx property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Vector of CDF values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.PiecewiseLinearDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.PiecewiseLinearDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.PiecewiseLinearDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.PiecewiseLinearDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
prob.PiecewiseLinearDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 241
prob.PiecewiseLinearDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.PiecewiseLinearDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.PiecewiseLinearDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.PiecewiseLinearDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.PiecewiseLinearDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the x and Fx
properties.


# name: <cell-element>
# type: sq_string
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# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
prob.PiecewiseLinearDistribution.PiecewiseLinearDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 419
prob.PiecewiseLinearDistribution: pd = PiecewiseLinearDistribution ( x , Fx )
prob.PiecewiseLinearDistribution: pd = PiecewiseLinearDistribution ()

Create a prob.PiecewiseLinearDistribution object.

x and Fx are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, x [0; 1] and Fx [0; 1] .

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
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# length: 49
Create a prob.PiecewiseLinearDistribution object.



# name: <cell-element>
# type: sq_string
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# length: 43
prob.PiecewiseLinearDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 361
prob.PiecewiseLinearDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 421
prob.PiecewiseLinearDistribution: p = cdf ( pd , x )
prob.PiecewiseLinearDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.PiecewiseLinearDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 259
prob.PiecewiseLinearDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.PiecewiseLinearDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.PiecewiseLinearDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 178
prob.PiecewiseLinearDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.PiecewiseLinearDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 186
prob.PiecewiseLinearDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.PiecewiseLinearDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.PiecewiseLinearDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1569
prob.PiecewiseLinearDistribution: plot ( pd )
prob.PiecewiseLinearDistribution: plot ( pd , Name , Value )
prob.PiecewiseLinearDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.PiecewiseLinearDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 742
prob.PiecewiseLinearDistribution: r = random ( pd )
prob.PiecewiseLinearDistribution: r = random ( pd , rows )
prob.PiecewiseLinearDistribution: r = random ( pd , rows , cols , &hellip;)
prob.PiecewiseLinearDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.PiecewiseLinearDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.PiecewiseLinearDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 538
prob.PiecewiseLinearDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd ) returns a probability distribution
t , which is the probability distribution pd truncated to the
specified interval with lower limit, lower , and upper limit,
upper . If pd is fitted to data with fitdist , the
returned probability distribution t is not fitted, does not contain
any data or estimated values, and it is as it has been created with the
makedist function, but it includes the truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.PiecewiseLinearDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.PiecewiseLinearDistribution.x


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.PiecewiseLinearDistribution: property x

Vector of x values

A numeric row vector of x values at which the CDF changes slope,
reported as a row whichever way it was given. You can access the
x property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Vector of x values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.PoissonDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1336
statistics: prob.PoissonDistribution

Poisson probability distribution object.

A prob.PoissonDistribution object consists of parameters, a model
description, and sample data for a Poisson probability distribution.

The Poisson distribution is a discrete probability distribution that
models the number of events occurring in a fixed interval of time or space,
given a constant average rate of occurrence. It is defined by the rate
parameter lambda .

There are several ways to create a prob.PoissonDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.PoissonDistribution ( lambda )
to create a Poisson distribution with fixed parameter value lambda .
Use the static method prob.PoissonDistribution.fit ( x ,
freq ) to fit a distribution to the data in x using
the same input arguments as the poissfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Poisson distribution can be found at
https://en.wikipedia.org/wiki/Poisson_distribution

See also:
fitdist,
makedist,
poisscdf,
poissinv,
poisspdf,
poissrnd,
poissfit,
poisslike,
poisstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Poisson probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.PoissonDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.PoissonDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.PoissonDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 740
prob.PoissonDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PoissonDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.PoissonDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.PoissonDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.PoissonDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.PoissonDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 422
prob.PoissonDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 1&times;1 numeric matrix containing the variance of the parameter
estimate. This matrix is only meaningful when the distribution was fitted
to data. If the distribution object was created with fixed parameters,
or a parameter of a fitted distribution is modified, then the
variance is zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.PoissonDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.PoissonDistribution: property ParameterDescription

Description of parameters

A 1&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.PoissonDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 278
prob.PoissonDistribution: property ParameterIsFixed

Flag for fixed parameters

A logical scalar specifying whether the parameter is fixed or estimated.
A true value corresponds to a fixed parameter, a false
value corresponds to a parameter estimate. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.PoissonDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.PoissonDistribution: property ParameterNames

Names of parameters

A 1&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.PoissonDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 282
prob.PoissonDistribution: property ParameterValues

Distribution parameter values

A 1&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the lambda property.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.PoissonDistribution.PoissonDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 357
prob.PoissonDistribution: pd = PoissonDistribution ( lambda )
prob.PoissonDistribution: pd = PoissonDistribution ()

Create a prob.PoissonDistribution object.

lambda is the distribution parameter, which the class help
describes. Called with no arguments the parameter takes its default,
lambda 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Create a prob.PoissonDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.PoissonDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 361
prob.PoissonDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. The first element contains the lower boundary,
the second element contains the upper boundary. This property is
read-only. You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 405
prob.PoissonDistribution: p = cdf ( pd , x )
prob.PoissonDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.PoissonDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 251
prob.PoissonDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.PoissonDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.PoissonDistribution.lambda


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.PoissonDistribution: property lambda

Rate parameter

A positive scalar value characterizing the rate of the
Poisson distribution. You can access the lambda
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
Rate parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.PoissonDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 170
prob.PoissonDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.PoissonDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 178
prob.PoissonDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.PoissonDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 224
prob.PoissonDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.PoissonDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 990
prob.PoissonDistribution: ci = paramci ( pd )
prob.PoissonDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.PoissonDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.PoissonDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1485
prob.PoissonDistribution: plot ( pd )
prob.PoissonDistribution: plot ( pd , Name , Value )
prob.PoissonDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions.
'Parent' An axes graphics object for the plot.
If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.PoissonDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2094
prob.PoissonDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.PoissonDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.PoissonDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.PoissonDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.PoissonDistribution: [ nlogL , param ] = proflik ( pd )
prob.PoissonDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Poisson distribution, pnum = 1 selects the
parameter lambda .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the user-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.PoissonDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 711
prob.PoissonDistribution: r = random ( pd )
prob.PoissonDistribution: r = random ( pd , rows )
prob.PoissonDistribution: r = random ( pd , rows , cols , &hellip;)
prob.PoissonDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, poissrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.PoissonDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.PoissonDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 546
prob.PoissonDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 176
prob.PoissonDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.ProbabilityDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 768
statistics: prob.ProbabilityDistribution

Abstract base class of the probability distribution objects.

It holds the behaviour every distribution object shares &ndash; how it is
displayed, how its parameter confidence intervals are computed, how it is
plotted and how a profile likelihood is taken &ndash; as protected methods, so
the 29 distribution classes inherit one implementation and no part of it is
reachable from outside them.

These helpers were ordinary files in a private directory until the
classes moved into the prob namespace. Octave does not resolve a
private directory from inside a package directory, for a classdef or
for a plain function, so the only way to keep them out of the public
interface is to make them protected methods of a shared base.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Abstract base class of the probability distribution objects.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.RayleighDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1522
statistics: prob.RayleighDistribution

Rayleigh probability distribution object.

A prob.RayleighDistribution object consists of parameters, a model
description, and sample data for a Rayleigh probability distribution.

The Rayleigh distribution is a continuous probability distribution for
nonnegative random variables. It is often used to model the magnitude of
a vector in two dimensions where the components are normally distributed
with zero mean and equal variance. It is defined by scale parameter
B .

B is the sigma of the usual mathematical notation. The
rayl* functions name the same quantity sigma ; this class
follows MATLAB.

There are several ways to create a prob.RayleighDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.RayleighDistribution ( B )
to create a Rayleigh distribution with fixed parameter value B .
Use the static method prob.RayleighDistribution.fit ( x ,
censor , freq ) to fit a distribution to the data in x
using the same input arguments as the raylfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Rayleigh distribution can be found at
https://en.wikipedia.org/wiki/Rayleigh_distribution

See also:
fitdist,
makedist,
raylcdf,
raylinv,
raylpdf,
raylrnd,
raylfit,
rayllike,
raylstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Rayleigh probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.RayleighDistribution.B


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.RayleighDistribution: property B

Scale parameter

A positive scalar value characterizing the scale of the
Rayleigh distribution. You can access the B
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.RayleighDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.RayleighDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.RayleighDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 741
prob.RayleighDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.RayleighDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.RayleighDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.RayleighDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.RayleighDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.RayleighDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 613
prob.RayleighDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
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# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
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prob.RayleighDistribution.ParameterDescription


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prob.RayleighDistribution: property ParameterDescription

Description of parameters

A cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.RayleighDistribution.ParameterIsFixed


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# length: 280
prob.RayleighDistribution: property ParameterIsFixed

Flag for fixed parameters

A logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.RayleighDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
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# length: 201
prob.RayleighDistribution: property ParameterNames

Names of parameters

A cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.RayleighDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 268
prob.RayleighDistribution: property ParameterValues

Distribution parameter values

A numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the B
property.


# name: <cell-element>
# type: sq_string
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# length: 29
Distribution parameter values



# name: <cell-element>
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# elements: 1
# length: 46
prob.RayleighDistribution.RayleighDistribution


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prob.RayleighDistribution: pd = RayleighDistribution ( B )
prob.RayleighDistribution: pd = RayleighDistribution ()

Create a prob.RayleighDistribution object.

B is the distribution parameter, which the class help describes.
Called with no arguments the parameter takes its default, B 1.

makedist is the usual way to create a distribution object.


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Create a prob.RayleighDistribution object.



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prob.RayleighDistribution.Truncation


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prob.RayleighDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



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# elements: 1
# length: 29
prob.RayleighDistribution.cdf


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prob.RayleighDistribution: p = cdf ( pd , x )
prob.RayleighDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



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prob.RayleighDistribution.icdf


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prob.RayleighDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


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Compute the inverse cumulative distribution function (iCDF).



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prob.RayleighDistribution.iqr


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prob.RayleighDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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Compute the interquartile range of a probability distribution.



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prob.RayleighDistribution.mean


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prob.RayleighDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


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Compute the mean of a probability distribution.



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prob.RayleighDistribution.median


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prob.RayleighDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


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Compute the median of a probability distribution.



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prob.RayleighDistribution.negloglik


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prob.RayleighDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


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Compute the negative loglikelihood of a probability distribution.



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prob.RayleighDistribution.paramci


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prob.RayleighDistribution: ci = paramci ( pd )
prob.RayleighDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.RayleighDistribution.pdf


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prob.RayleighDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


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Compute the probability distribution function (PDF).



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prob.RayleighDistribution.plot


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prob.RayleighDistribution: plot ( pd )
prob.RayleighDistribution: plot ( pd , Name , Value )
prob.RayleighDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


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Plot a probability distribution object.



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prob.RayleighDistribution.proflik


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prob.RayleighDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.RayleighDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.RayleighDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.RayleighDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.RayleighDistribution: [ nlogL , param ] = proflik ( pd )
prob.RayleighDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Rayleigh distribution, pnum = 1 selects
the parameter B .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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prob.RayleighDistribution.random


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prob.RayleighDistribution: r = random ( pd )
prob.RayleighDistribution: r = random ( pd , rows )
prob.RayleighDistribution: r = random ( pd , rows , cols , &hellip;)
prob.RayleighDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
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# length: 64
Generate random arrays from the probability distribution object.



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prob.RayleighDistribution.std


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prob.RayleighDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


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Compute the standard deviation of a probability distribution.



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prob.RayleighDistribution.truncate


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prob.RayleighDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


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Truncate a probability distribution.



# name: <cell-element>
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prob.RayleighDistribution.var


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prob.RayleighDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
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Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
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# length: 23
prob.RicianDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1258
statistics: prob.RicianDistribution

Rician probability distribution object.

A prob.RicianDistribution object consists of parameters, a model
description, and sample data for a Rician probability distribution.

The Rician distribution is a continuous probability distribution that
models the magnitude of a signal in the presence of Gaussian noise. It is
defined by noncentrality parameter s and scale parameter sigma .

There are several ways to create a prob.RicianDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.RicianDistribution ( s , sigma )
to create a Rician distribution with fixed parameter values s and
sigma .
Use the static method prob.RicianDistribution.fit ( x ,
censor , freq , options ) to fit a distribution to data
x .

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Rician distribution can be found at
https://en.wikipedia.org/wiki/Rice_distribution

See also:
fitdist,
makedist,
ricecdf,
riceinv,
ricepdf,
ricernd,
ricefit,
ricelike,
ricestat


# name: <cell-element>
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Rician probability distribution object.



# name: <cell-element>
# type: sq_string
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prob.RicianDistribution.DistributionName


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prob.RicianDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
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Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.RicianDistribution.InputData


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# type: sq_string
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# length: 739
prob.RicianDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
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Data used for fitting a probability distribution



# name: <cell-element>
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prob.RicianDistribution.IsTruncated


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prob.RicianDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
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Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.RicianDistribution.NumParameters


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# type: sq_string
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# length: 202
prob.RicianDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
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Number of parameters



# name: <cell-element>
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# length: 43
prob.RicianDistribution.ParameterCovariance


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# length: 621
prob.RicianDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.RicianDistribution.ParameterDescription


# name: <cell-element>
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# length: 232
prob.RicianDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
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# elements: 1
# length: 40
prob.RicianDistribution.ParameterIsFixed


# name: <cell-element>
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# length: 288
prob.RicianDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.RicianDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.RicianDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.RicianDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
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# length: 288
prob.RicianDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the s and sigma
properties.


# name: <cell-element>
# type: sq_string
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# length: 29
Distribution parameter values



# name: <cell-element>
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# elements: 1
# length: 42
prob.RicianDistribution.RicianDistribution


# name: <cell-element>
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prob.RicianDistribution: pd = RicianDistribution ( s , sigma )
prob.RicianDistribution: pd = RicianDistribution ()

Create a prob.RicianDistribution object.

s and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, s 1 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
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Create a prob.RicianDistribution object.



# name: <cell-element>
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prob.RicianDistribution.Truncation


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prob.RicianDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
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# elements: 1
# length: 27
prob.RicianDistribution.cdf


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prob.RicianDistribution: p = cdf ( pd , x )
prob.RicianDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



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prob.RicianDistribution.icdf


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prob.RicianDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


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# length: 60
Compute the inverse cumulative distribution function (iCDF).



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# length: 27
prob.RicianDistribution.iqr


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prob.RicianDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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Compute the interquartile range of a probability distribution.



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prob.RicianDistribution.mean


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prob.RicianDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


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Compute the mean of a probability distribution.



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# length: 30
prob.RicianDistribution.median


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# length: 177
prob.RicianDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


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# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.RicianDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 223
prob.RicianDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.RicianDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 988
prob.RicianDistribution: ci = paramci ( pd )
prob.RicianDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.RicianDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.RicianDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.RicianDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1542
prob.RicianDistribution: plot ( pd )
prob.RicianDistribution: plot ( pd , Name , Value )
prob.RicianDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.RicianDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2123
prob.RicianDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.RicianDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.RicianDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.RicianDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.RicianDistribution: [ nlogL , param ] = proflik ( pd )
prob.RicianDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Rician distribution, pnum = 1 selects the
parameter s and pnum = 2 selects the parameter
sigma .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.RicianDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 706
prob.RicianDistribution: r = random ( pd )
prob.RicianDistribution: r = random ( pd , rows )
prob.RicianDistribution: r = random ( pd , rows , cols , &hellip;)
prob.RicianDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, ricernd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.RicianDistribution.s


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.RicianDistribution: property s

Noncentrality parameter

A non-negative scalar value characterizing the noncentrality of the
Rician distribution. You can access the s property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
Noncentrality parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.RicianDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.RicianDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the Rician
distribution. You can access the sigma property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.RicianDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.RicianDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.RicianDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 545
prob.RicianDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.RicianDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.RicianDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.StableDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1774
statistics: prob.StableDistribution

Stable probability distribution object.

A prob.StableDistribution object consists of parameters, a model
description, and sample data for a stable probability distribution.

The stable distribution is a continuous probability distribution family
closed under linear combinations, generalizing the normal, Cauchy, and Levy
distributions. It is parameterized, in the Nolan S0
parameterization, by a tail index (first shape parameter) alpha in
(0, 2] , a skewness (second shape parameter) beta in
[-1, 1] , a scale parameter gam greater than zero, and a
location parameter delta .

There are several ways to create a prob.StableDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.StableDistribution ( alpha ,
beta , gam , delta ) to create a stable distribution with
fixed parameter values alpha , beta , gam , and delta .
Use the static method prob.StableDistribution.fit ( x ,
alpha , freq , options ) to fit a distribution to the data
in x using the same input arguments as the stblfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Fitting is by maximum likelihood. Because the stable density has no closed
form, it is evaluated by numerical inversion of the characteristic function,
which makes fitting considerably slower than for the closed-form
distributions.

Further information about the stable distribution can be found at
https://en.wikipedia.org/wiki/Stable_distribution

See also:
fitdist,
makedist,
stblpdf,
stblcdf,
stblinv,
stblrnd,
stblfit,
stbllike


# name: <cell-element>
# type: sq_string
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# length: 39
Stable probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.StableDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.StableDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.StableDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 260
prob.StableDistribution: property InputData

Data used for fitting the distribution

A structure containing the data used to fit the distribution. It is empty
unless the distribution was fitted with fitdist or the static
fit method. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Data used for fitting the distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.StableDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.StableDistribution: property IsTruncated

Flag for truncated distribution

A logical scalar that is true when the distribution is truncated. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
Flag for truncated distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.StableDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.StableDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.StableDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 222
prob.StableDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 4&times;4 numeric matrix containing the variance-covariance of the
distribution parameters. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.StableDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 232
prob.StableDistribution: property ParameterDescription

Description of parameters

A 4&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.StableDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.StableDistribution: property ParameterIsFixed

Flags for fixed parameters

A 4&times;1 logical vector specifying which parameters are held fixed
rather than estimated. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
Flags for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.StableDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.StableDistribution: property ParameterNames

Names of parameters

A 4&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.StableDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 303
prob.StableDistribution: property ParameterValues

Distribution parameter values

A 4&times;1 numeric vector containing the values of the distribution
parameters, matching the order in ParameterNames . This property
is read-only; use dot name assignment on the alpha , beta ,
gam , and delta properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.StableDistribution.StableDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 425
prob.StableDistribution: pd = StableDistribution ( alpha , beta , gam , delta )
prob.StableDistribution: pd = StableDistribution ()

Create a prob.StableDistribution object.

alpha , beta , gam and delta are the distribution
parameters, which the class help describes. Called with no arguments the
parameters take their defaults, alpha 2, beta 0, gam 1
and delta 0.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Create a prob.StableDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.StableDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
prob.StableDistribution: property Truncation

Truncation interval

A two-element numeric vector with the truncation interval, if the
distribution is truncated. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.StableDistribution.alpha


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.StableDistribution: property alpha

Tail index (first shape parameter)

A scalar value in the range (0, 2] characterizing the tail
behaviour of the stable distribution. You can access the alpha
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
Tail index (first shape parameter)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.beta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.StableDistribution: property beta

Skewness (second shape parameter)

A scalar value in the range [-1, 1] characterizing the skewness of
the stable distribution. You can access the beta property using
dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
Skewness (second shape parameter)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 326
prob.StableDistribution: p = cdf ( pd , x )
prob.StableDistribution: p = cdf ( pd , x , "upper" )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x . The optional "upper" flag computes the upper tail
probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.StableDistribution.delta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.StableDistribution: property delta

Location parameter

A scalar value characterizing the location of the stable distribution.
You can access the delta property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.gam


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.StableDistribution: property gam

Scale parameter

A positive scalar value characterizing the scale of the stable
distribution. You can access the gam property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 250
prob.StableDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.StableDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.StableDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd . The mean is NaN for
alpha <= 1 , where it is undefined.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.StableDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.StableDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.StableDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 280
prob.StableDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd . It
returns an empty value when pd is not fitted to data.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.StableDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1002
prob.StableDistribution: ci = paramci ( pd )
prob.StableDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise the parameter values are returned in both rows.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.StableDistribution: y = pdf ( pd , x )

Compute the probability density function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the probability density function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 378
prob.StableDistribution: plot ( pd )
prob.StableDistribution: plot ( pd , Name , Value )
prob.StableDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots the probability density function (PDF) of
the probability distribution object pd . Name-value pair arguments
select the plotted function and its appearance, as documented in
__plot__ .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.StableDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1909
prob.StableDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.StableDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.StableDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.StableDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.StableDistribution: [ nlogL , param ] = proflik ( pd )
prob.StableDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the stable distribution, pnum = 1 selects the tail index
alpha , pnum = 2 selects the skewness beta ,
pnum = 3 selects the scale gam , and
pnum = 4 selects the location delta .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.StableDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 397
prob.StableDistribution: r = random ( pd )
prob.StableDistribution: r = random ( pd , rows )
prob.StableDistribution: r = random ( pd , rows , cols , &hellip;)
prob.StableDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd , following the size conventions of
stblrnd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 253
prob.StableDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd . It is NaN for
alpha < 2 , where the variance is infinite.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.StableDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 248
prob.StableDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns
the probability distribution pd truncated to the interval with
lower limit lower and upper limit upper .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.StableDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the probability
distribution object, pd . It is NaN for alpha <
2 , where the variance is infinite.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.TriangularDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1005
statistics: prob.TriangularDistribution

Triangular probability distribution object.

A prob.TriangularDistribution object consists of parameters, a model
description, and sample data for a triangular probability distribution.

The triangular distribution uses the following parameters.

Parameter Description Support
A Lower limit -Inf < A < Inf
B Peak location A <= B <= C
C Upper limit C > A

There are several ways to create a prob.TriangularDistribution object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor prob.TriangularDistribution ( A , B ,
C ) to create a triangular distribution with specified parameter
values A , B , and C .

It is highly recommended to use makedist function to create
probability distribution objects, instead of the constructor.

Further information about the triangular distribution can be found
at https://en.wikipedia.org/wiki/Triangular_distribution

See also:
makedist,
tricdf,
triinv,
tripdf,
trirnd,
tristat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Triangular probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.TriangularDistribution.A


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.TriangularDistribution: property A

Lower limit parameter

A scalar value characterizing the lower limit of the
triangular distribution. You can access the A
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Lower limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.TriangularDistribution.B


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.TriangularDistribution: property B

Peak location parameter

A scalar value characterizing the peak location of the
triangular distribution. You can access the B
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
Peak location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.TriangularDistribution.C


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.TriangularDistribution: property C

Upper limit parameter

A scalar value characterizing the upper limit of the
triangular distribution. You can access the C
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Upper limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.TriangularDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.TriangularDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.TriangularDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.TriangularDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.TriangularDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.TriangularDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.TriangularDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 236
prob.TriangularDistribution: property ParameterDescription

Description of parameters

A 3&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.TriangularDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.TriangularDistribution: property ParameterNames

Names of parameters

A 3&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.TriangularDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.TriangularDistribution: property ParameterValues

Distribution parameter values

A 3&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the A , B , and
C properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.TriangularDistribution.TriangularDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 395
prob.TriangularDistribution: pd = TriangularDistribution ( A , B , C )
prob.TriangularDistribution: pd = TriangularDistribution ()

Create a prob.TriangularDistribution object.

A , B and C are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, A 0, B 0.5 and C 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Create a prob.TriangularDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.TriangularDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 356
prob.TriangularDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 411
prob.TriangularDistribution: p = cdf ( pd , x )
prob.TriangularDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.TriangularDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 254
prob.TriangularDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.TriangularDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.TriangularDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.TriangularDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.TriangularDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 181
prob.TriangularDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.TriangularDistribution: y = pdf ( pd , x )

Compute the probability density function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the probability density function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.TriangularDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1135
prob.TriangularDistribution: plot ( pd )
prob.TriangularDistribution: plot ( pd , Name , Value )
prob.TriangularDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd .

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF).
'cdf' plots the cumulative density function (CDF).
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, this option is ignored.
'Parent' An axes graphics object for the plot.
If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.TriangularDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 721
prob.TriangularDistribution: r = random ( pd )
prob.TriangularDistribution: r = random ( pd , rows )
prob.TriangularDistribution: r = random ( pd , rows , cols , &hellip;)
prob.TriangularDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, trirnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.TriangularDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.TriangularDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 306
prob.TriangularDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.TriangularDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.UniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1160
statistics: prob.UniformDistribution

Continuous uniform probability distribution object.

A prob.UniformDistribution object consists of parameters, a model
description, and sample data for a uniform probability distribution.

The uniform distribution is a continuous probability distribution that
models random variables that are equally likely to take any value within a
specified interval defined by the lower limit Lower and upper limit
Upper .

There are several ways to create a prob.UniformDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.UniformDistribution ( Lower ,
Upper ) to create a uniform distribution with fixed parameter
values Lower and Upper .

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor.

Further information about the continuous uniform distribution can be found
at https://en.wikipedia.org/wiki/Continuous_uniform_distribution

See also:
fitdist,
makedist,
unifcdf,
unifinv,
unifpdf,
unifrnd,
unifit,
unifstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Continuous uniform probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.UniformDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.UniformDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.UniformDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.UniformDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.UniformDistribution.Lower


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.UniformDistribution: property Lower

Lower limit parameter

A scalar value characterizing the lower bound of the uniform
distribution. You can access the Lower property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Lower limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.UniformDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.UniformDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.UniformDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.UniformDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.UniformDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.UniformDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.UniformDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 293
prob.UniformDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the Lower and Upper
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.UniformDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 353
prob.UniformDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.UniformDistribution.UniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 389
prob.UniformDistribution: pd = UniformDistribution ( Lower , Upper )
prob.UniformDistribution: pd = UniformDistribution ()

Create a prob.UniformDistribution object.

Lower and Upper are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, Lower 0 and Upper 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Create a prob.UniformDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.UniformDistribution.Upper


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.UniformDistribution: property Upper

Upper limit parameter

A scalar value characterizing the upper bound of the uniform
distribution. You can access the Upper property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Upper limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 405
prob.UniformDistribution: p = cdf ( pd , x )
prob.UniformDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.UniformDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 251
prob.UniformDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.UniformDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.UniformDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 170
prob.UniformDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


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Compute the mean of a probability distribution.



# name: <cell-element>
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prob.UniformDistribution.median


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prob.UniformDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
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Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.pdf


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# type: sq_string
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prob.UniformDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
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Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
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prob.UniformDistribution.plot


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prob.UniformDistribution: plot ( pd )
prob.UniformDistribution: plot ( pd , Name , Value )
prob.UniformDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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Plot a probability distribution object.



# name: <cell-element>
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prob.UniformDistribution.random


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prob.UniformDistribution: r = random ( pd )
prob.UniformDistribution: r = random ( pd , rows )
prob.UniformDistribution: r = random ( pd , rows , cols , &hellip;)
prob.UniformDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, unifrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
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# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
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# length: 28
prob.UniformDistribution.std


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prob.UniformDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
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Compute the standard deviation of a probability distribution.



# name: <cell-element>
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# length: 33
prob.UniformDistribution.truncate


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prob.UniformDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
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Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.var


# name: <cell-element>
# type: sq_string
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prob.UniformDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
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Compute the variance of a probability distribution.



# name: <cell-element>
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prob.WeibullDistribution


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statistics: prob.WeibullDistribution

Weibull probability distribution object.

A prob.WeibullDistribution object consists of parameters, a model
description, and sample data for a Weibull probability distribution.

The Weibull distribution is a continuous probability distribution that
models the time to failure of materials or the lifetime of mechanical
systems. It is defined by scale parameter A and shape
parameter B .

A is the lambda of the usual mathematical notation and
B is its k . The wbl* functions name the same two
quantities lambda and k ; this class follows MATLAB.

There are several ways to create a prob.WeibullDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.WeibullDistribution ( A ,
B ) to create a Weibull distribution with fixed parameter
values A and B .
Use the static method prob.WeibullDistribution.fit ( x ,
alpha , censor , freq ) to fit a distribution to the
data in x using the same input arguments as the wblfit
function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Weibull distribution can be found at
https://en.wikipedia.org/wiki/Weibull_distribution

See also:
fitdist,
makedist,
wblcdf,
wblinv,
wblpdf,
wblrnd,
wblfit,
wbllike,
wblstat


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Weibull probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
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prob.WeibullDistribution.A


# name: <cell-element>
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prob.WeibullDistribution: property A

Scale parameter

A positive scalar value characterizing the scale of the
Weibull distribution. You can access the A
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.WeibullDistribution.B


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.WeibullDistribution: property B

Shape parameter

A positive scalar value characterizing the shape of the
Weibull distribution. You can access the B
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.WeibullDistribution.DistributionName


# name: <cell-element>
# type: sq_string
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# length: 190
prob.WeibullDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.WeibullDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 740
prob.WeibullDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
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Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.WeibullDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
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prob.WeibullDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
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# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.WeibullDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.WeibullDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
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# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.WeibullDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 622
prob.WeibullDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 2&times;2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.WeibullDistribution.ParameterDescription


# name: <cell-element>
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# length: 233
prob.WeibullDistribution: property ParameterDescription

Description of parameters

A 2&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
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# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.WeibullDistribution.ParameterIsFixed


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prob.WeibullDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.WeibullDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.WeibullDistribution: property ParameterNames

Names of parameters

A 2&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.WeibullDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 285
prob.WeibullDistribution: property ParameterValues

Distribution parameter values

A 2&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the A and B
properties.


# name: <cell-element>
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# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.WeibullDistribution.Truncation


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prob.WeibullDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
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Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.WeibullDistribution.WeibullDistribution


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prob.WeibullDistribution: pd = WeibullDistribution ( A , B )
prob.WeibullDistribution: pd = WeibullDistribution ()

Create a prob.WeibullDistribution object.

A and B are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
A 1 and B 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
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Create a prob.WeibullDistribution object.



# name: <cell-element>
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prob.WeibullDistribution.cdf


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prob.WeibullDistribution: p = cdf ( pd , x )
prob.WeibullDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



# name: <cell-element>
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prob.WeibullDistribution.icdf


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prob.WeibullDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
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# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
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# length: 28
prob.WeibullDistribution.iqr


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# type: sq_string
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# length: 198
prob.WeibullDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


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# type: sq_string
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Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
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# length: 29
prob.WeibullDistribution.mean


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prob.WeibullDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


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Compute the mean of a probability distribution.



# name: <cell-element>
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prob.WeibullDistribution.median


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prob.WeibullDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


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Compute the median of a probability distribution.



# name: <cell-element>
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prob.WeibullDistribution.negloglik


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# length: 224
prob.WeibullDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
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Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.WeibullDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 990
prob.WeibullDistribution: ci = paramci ( pd )
prob.WeibullDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


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Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
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# length: 28
prob.WeibullDistribution.pdf


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# type: sq_string
# elements: 1
# length: 211
prob.WeibullDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
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Compute the probability distribution function (PDF).



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prob.WeibullDistribution.plot


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prob.WeibullDistribution: plot ( pd )
prob.WeibullDistribution: plot ( pd , Name , Value )
prob.WeibullDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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Plot a probability distribution object.



# name: <cell-element>
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prob.WeibullDistribution.proflik


# name: <cell-element>
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# length: 2126
prob.WeibullDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.WeibullDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.WeibullDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.WeibullDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.WeibullDistribution: [ nlogL , param ] = proflik ( pd )
prob.WeibullDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the Weibull distribution, pnum = 1 selects the
parameter A and pnum = 2 selects the
parameter B .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



# name: <cell-element>
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# length: 31
prob.WeibullDistribution.random


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prob.WeibullDistribution: r = random ( pd )
prob.WeibullDistribution: r = random ( pd , rows )
prob.WeibullDistribution: r = random ( pd , rows , cols , &hellip;)
prob.WeibullDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, wblrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
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# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
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# length: 28
prob.WeibullDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.WeibullDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


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Compute the standard deviation of a probability distribution.



# name: <cell-element>
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prob.WeibullDistribution.truncate


# name: <cell-element>
# type: sq_string
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# length: 546
prob.WeibullDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
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Truncate a probability distribution.



# name: <cell-element>
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# length: 28
prob.WeibullDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 176
prob.WeibullDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.tLocationScaleDistribution


# name: <cell-element>
# type: sq_string
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# length: 1588
statistics: prob.tLocationScaleDistribution

Location-Scale Student&rsquo;s T probability distribution object.

A prob.tLocationScaleDistribution object consists of parameters, a model
description, and sample data for a location-scale Student&rsquo;s T probability
distribution.

The location-scale Student&rsquo;s T distribution is a continuous probability
distribution that generalizes the standard Student&rsquo;s T distribution by
including location and scale parameters. It is defined by location
parameter
mu , scale parameter sigma , and degrees of freedom nu .

There are several ways to create a prob.tLocationScaleDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.tLocationScaleDistribution ( mu ,
sigma , nu ) to create a location-scale Student&rsquo;s T distribution
with fixed parameter values mu , sigma , and nu .
Use the static method prob.tLocationScaleDistribution.fit ( x ,
censor , freq , options ) to fit a distribution to the data
in x using the same input arguments as the tlsfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the location-scale Student&rsquo;s T distribution can
be found at
https://en.wikipedia.org/wiki/Student%27s_t-distribution#Location-scale_t_distribution

See also:
fitdist,
makedist,
tlscdf,
tlsinv,
tlspdf,
tlsrnd,
tlsfit,
tlslike,
tlsstat


# name: <cell-element>
# type: sq_string
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# length: 59
Location-Scale Student's T probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.tLocationScaleDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.tLocationScaleDistribution: property DistributionName

Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.tLocationScaleDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 747
prob.tLocationScaleDistribution: property InputData

Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
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# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.tLocationScaleDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
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# length: 217
prob.tLocationScaleDistribution: property IsTruncated

Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
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# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.tLocationScaleDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.tLocationScaleDistribution: property NumParameters

Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.tLocationScaleDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 629
prob.tLocationScaleDistribution: property ParameterCovariance

Covariance matrix of the parameter estimates

A 3&times;3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.tLocationScaleDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 240
prob.tLocationScaleDistribution: property ParameterDescription

Description of parameters

A 3&times;1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.tLocationScaleDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 296
prob.tLocationScaleDistribution: property ParameterIsFixed

Flag for fixed parameters

A 1&times;3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.tLocationScaleDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.tLocationScaleDistribution: property ParameterNames

Names of parameters

A 3&times;1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.tLocationScaleDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 304
prob.tLocationScaleDistribution: property ParameterValues

Distribution parameter values

A 3&times;1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu , sigma , and
nu properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.tLocationScaleDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 360
prob.tLocationScaleDistribution: property Truncation

Truncation interval

A 1&times;2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.cdf


# name: <cell-element>
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# elements: 1
# length: 419
prob.tLocationScaleDistribution: p = cdf ( pd , x )
prob.tLocationScaleDistribution: p = cdf ( pd , x , 'upper' )

Compute the cumulative distribution function (CDF).

p = cdf ( pd , x ) computes the CDF of the
probability distribution object, pd , evaluated at the values in
x .

p = cdf (&hellip;, 'upper' ) returns the complement of
the CDF of the probability distribution object, pd , evaluated at
the values in x .


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Compute the cumulative distribution function (CDF).



# name: <cell-element>
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prob.tLocationScaleDistribution.icdf


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# type: sq_string
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# length: 258
prob.tLocationScaleDistribution: x = icdf ( pd , p )

Compute the inverse cumulative distribution function (iCDF).

x = icdf ( pd , p ) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd ,
evaluated at the values in p .


# name: <cell-element>
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# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.iqr


# name: <cell-element>
# type: sq_string
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# length: 205
prob.tLocationScaleDistribution: r = iqr ( pd )

Compute the interquartile range of a probability distribution.

r = iqr ( pd ) computes the interquartile range of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.tLocationScaleDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.tLocationScaleDistribution: m = mean ( pd )

Compute the mean of a probability distribution.

m = mean ( pd ) computes the mean of the probability
distribution object, pd .


# name: <cell-element>
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# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
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# elements: 1
# length: 38
prob.tLocationScaleDistribution.median


# name: <cell-element>
# type: sq_string
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# length: 185
prob.tLocationScaleDistribution: m = median ( pd )

Compute the median of a probability distribution.

m = median ( pd ) computes the median of the probability
distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.tLocationScaleDistribution.mu


# name: <cell-element>
# type: sq_string
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# length: 220
prob.tLocationScaleDistribution: property mu

Location parameter

A scalar value characterizing the location of the
location-scale Student&rsquo;s T distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.tLocationScaleDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 231
prob.tLocationScaleDistribution: nlogL = negloglik ( pd )

Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik ( pd ) computes the negative
loglikelihood of the probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.tLocationScaleDistribution.nu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 239
prob.tLocationScaleDistribution: property nu

Degrees of freedom

A positive scalar value characterizing the degrees of freedom of the
location-scale Student&rsquo;s T distribution. You can access the nu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Degrees of freedom



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.tLocationScaleDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1004
prob.tLocationScaleDistribution: ci = paramci ( pd )
prob.tLocationScaleDistribution: ci = paramci ( pd , Name , Value )

Compute the confidence intervals for probability distribution parameters.

ci = paramci ( pd ) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd .

ci = paramci ( pd , Name , Value ) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [] , is returned.


# name: <cell-element>
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# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.pdf


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# type: sq_string
# elements: 1
# length: 218
prob.tLocationScaleDistribution: y = pdf ( pd , x )

Compute the probability distribution function (PDF).

y = pdf ( pd , x ) computes the PDF of the
probability distribution object, pd , evaluated at the values in
x .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.tLocationScaleDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1566
prob.tLocationScaleDistribution: plot ( pd )
prob.tLocationScaleDistribution: plot ( pd , Name , Value )
prob.tLocationScaleDistribution: h = plot (&hellip;)

Plot a probability distribution object.

plot ( pd ) plots a probability density function (PDF) of the
probability distribution object pd . If pd contains data,
which have been fitted by fitdist , the PDF is superimposed over a
histogram of the data.

plot ( pd , Name , Value ) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true , respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (&hellip;) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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Plot a probability distribution object.



# name: <cell-element>
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# elements: 1
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prob.tLocationScaleDistribution.proflik


# name: <cell-element>
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# length: 2236
prob.tLocationScaleDistribution: [ nlogL , param ] = proflik ( pd , pnum )
prob.tLocationScaleDistribution: [ nlogL , param ] = proflik ( pd , pnum , 'Display' , display )
prob.tLocationScaleDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam )
prob.tLocationScaleDistribution: [ nlogL , param ] = proflik ( pd , pnum , setparam , 'Display' , display )
prob.tLocationScaleDistribution: [ nlogL , param ] = proflik ( pd )
prob.tLocationScaleDistribution: [ nlogL , param , other ] = proflik (&hellip;)

Profile likelihood function for a probability distribution object.

[ nlogL , param ] = proflik ( pd , pnum )
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum . By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[ nlogL , param ] = proflik ( pd , pnum ,
'Display' , 'on' ) also plots the profile likelihood
against the default range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam ) defines a user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd , pnum ,
setparam , 'Display' , 'on' ) also plots the profile
likelihood against the user-defined range of the selected parameter.

[ nlogL , param ] = proflik ( pd ) selects the
first parameter that is not fixed.

[ nlogL , param , other ] = proflik (&hellip;) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param . A fixed parameter keeps its own value.

For the location-scale Student&rsquo;s T distribution, pnum = 1
selects the parameter mu , pnum = 2 selects the
parameter sigma , and pnum = 3 selects the
parameter nu .

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
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Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.tLocationScaleDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 737
prob.tLocationScaleDistribution: r = random ( pd )
prob.tLocationScaleDistribution: r = random ( pd , rows )
prob.tLocationScaleDistribution: r = random ( pd , rows , cols , &hellip;)
prob.tLocationScaleDistribution: r = random ( pd , [ sz ])

Generate random arrays from the probability distribution object.

r = random ( pd ) returns a random number from the
distribution object pd .

When called with a single size argument, tlsrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.tLocationScaleDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 229
prob.tLocationScaleDistribution: property sigma

Scale parameter

A positive scalar value characterizing the scale of the location-scale
Student&rsquo;s T distribution. You can access the sigma property using
dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.tLocationScaleDistribution: s = std ( pd )

Compute the standard deviation of a probability distribution.

s = std ( pd ) computes the standard deviation of the
probability distribution object, pd .


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
prob.tLocationScaleDistribution.tLocationScaleDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 431
prob.tLocationScaleDistribution: pd = tLocationScaleDistribution ( mu , sigma , nu )
prob.tLocationScaleDistribution: pd = tLocationScaleDistribution ()

Create a prob.tLocationScaleDistribution object.

mu , sigma and nu are the distribution parameters, which
the class help describes. Called with no arguments the parameters take
their defaults, mu 0, sigma 1 and nu 5.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
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# length: 48
Create a prob.tLocationScaleDistribution object.



# name: <cell-element>
# type: sq_string
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# length: 40
prob.tLocationScaleDistribution.truncate


# name: <cell-element>
# type: sq_string
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# length: 553
prob.tLocationScaleDistribution: t = truncate ( pd , lower , upper )

Truncate a probability distribution.

t = truncate ( pd , lower , upper ) returns a
probability distribution t , which is the probability distribution
pd truncated to the specified interval with lower limit,
lower , and upper limit, upper . If pd is fitted to data
with fitdist , the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
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# length: 36
Truncate a probability distribution.



# name: <cell-element>
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prob.tLocationScaleDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 183
prob.tLocationScaleDistribution: v = var ( pd )

Compute the variance of a probability distribution.

v = var ( pd ) computes the variance of the
probability distribution object, pd .


# name: <cell-element>
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# length: 51
Compute the variance of a probability distribution.





