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betafit


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statistics: paramhat = betafit ( x )
statistics: [ paramhat , paramci ] = betafit ( x )
statistics: [ paramhat , paramci ] = betafit ( x , alpha )
statistics: [ paramhat , paramci ] = betafit ( x , alpha , freq )
statistics: [ paramhat , paramci ] = betafit ( x , alpha , options )
statistics: [ paramhat , paramci ] = betafit ( x , alpha , freq , options )

Estimate parameters and confidence intervals for the Beta distribution.

paramhat = betafit ( x ) returns the maximum likelihood
estimates of the parameters of the Beta distribution given the data in vector
x . paramhat ([1, 2]) corresponds to the α and
β shape parameters, respectively. Missing values, NaNs , are
ignored.

[ paramhat , paramci ] = betafit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = betafit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals of the estimated
parameter. By default, the optional argument alpha is 0.05
corresponding to 95% confidence intervals.

[&hellip;] = betafit ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

[ paramhat , paramci ] = betafit ( x , alpha ,
options ) specifies control parameters for the iterative algorithm used
to compute ML estimates with the fminsearch function. options
is a structure with the following fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

The Beta distribution is defined on the open interval (0,1) . However,
betafit can also compute the unbounded beta likelihood function for
data that include exact zeros or ones. In such cases, zeros and ones are
treated as if they were values that have been left-censored at
sqrt (realmin) or right-censored at 1 - eps/2 , respectively.

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

See also:
betacdf,
betainv,
betapdf,
betarnd,
betalike,
betastat


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Estimate parameters and confidence intervals for the Beta distribution.



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betalike


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statistics: nlogL = betalike ( params , x )
statistics: [ nlogL , avar ] = betalike ( params , x )

Negative log-likelihood for the Beta distribution.

nlogL = betalike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the Beta distribution
with (1) shape parameter α and (2) shape parameter β given in
the two-element vector params . Both parameters must be positive real
numbers and the data in the range [0,1] . Out of range parameters or
data return NaN .

[ nlogL , avar ] = betalike ( params , x ) returns
the inverse of Fisher&rsquo;s information matrix, avar . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = betalike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

The Beta distribution is defined on the open interval (0,1) . However,
betafit can also compute the unbounded beta likelihood function for
data that include exact zeros or ones. In such cases, zeros and ones are
treated as if they were values that have been left-censored at
sqrt (realmin) or right-censored at 1 - eps/2 , respectively.

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

See also:
betacdf,
betainv,
betapdf,
betarnd,
betafit,
betastat


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Negative log-likelihood for the Beta distribution.



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binofit


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statistics: pshat = binofit ( x , n )
statistics: [ pshat , psci ] = binofit ( x , n )
statistics: [ pshat , psci ] = binofit ( x , n , alpha )

Estimate parameter and confidence intervals for the binomial distribution.

pshat = binofit ( x , n ) returns the maximum
likelihood estimate (MLE) of the probability of success for the binomial
distribution. x and n are scalars containing the number of
successes and the number of trials, respectively. If x and n are
vectors, binofit returns a vector of estimates whose i -th
element is the parameter estimate for x (i) and n (i). A scalar
value for x or n is expanded to the same size as the other input.

[ pshat , psci ] = binofit ( x , n , alpha )
also returns the 100 * (1 - alpha ) percent confidence intervals
of the estimated parameter. By default, the optional argument alpha
is 0.05 corresponding to 95% confidence intervals.

binofit treats a vector x as a collection of measurements from
separate samples, and returns a vector of estimates. If you want to treat
x as a single sample and compute a single parameter estimate and
confidence interval, use binofit (sum ( x ), sum ( n )) when
n is a vector, and
binofit (sum ( x ), n * length ( x )) when n is a
scalar.

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

See also:
binocdf,
binoinv,
binopdf,
binornd,
binolike,
binostat


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Estimate parameter and confidence intervals for the binomial distribution.



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binolike


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statistics: nlogL = binolike ( params , x )
statistics: [ nlogL , acov ] = binolike ( params , x )
statistics: [&hellip;] = binolike ( params , x , freq )

Negative log-likelihood for the binomial distribution.

nlogL = binolike ( params , x ) returns the negative
log likelihood of the binomial distribution with (1) parameter n and
(2) parameter ps , given in the two-element vector params , where
n is the number of trials and ps is the probability of success,
given the number of successes in x . Unlike binofit , which
handles each element in x independently, binolike returns the
negative log likelihood of the entire vector x .

[ nlogL , acov ] = binolike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = binolike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) .

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

See also:
binocdf,
binoinv,
binopdf,
binornd,
binofit,
binostat


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Negative log-likelihood for the binomial distribution.



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bisafit


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statistics: paramhat = bisafit ( x )
statistics: [ paramhat , paramci ] = bisafit ( x )
statistics: [ paramhat , paramci ] = bisafit ( x , alpha )
statistics: [&hellip;] = bisafit ( x , alpha , censor )
statistics: [&hellip;] = bisafit ( x , alpha , censor , freq )
statistics: [&hellip;] = bisafit ( x , alpha , censor , freq , options )

Estimate mean and confidence intervals for the Birnbaum-Saunders
distribution.

muhat = bisafit ( x ) returns the maximum likelihood
estimates of the parameters of the Birnbaum-Saunders distribution given the
data in x . paramhat (1) is the scale parameter,
beta , and paramhat (2) is the shape parameter,
gamma .

[ paramhat , paramci ] = bisafit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = bisafit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = bisafit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = bisafit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = bisafit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute ML estimates with the
fminsearch function. options is a structure with the following
fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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

See also:
bisacdf,
bisainv,
bisapdf,
bisarnd,
bisalike,
bisastat


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Estimate mean and confidence intervals for the Birnbaum-Saunders distribution.



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bisalike


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statistics: nlogL = bisalike ( params , x )
statistics: [ nlogL , acov ] = bisalike ( params , x )
statistics: [&hellip;] = bisalike ( params , x , censor )
statistics: [&hellip;] = bisalike ( params , x , censor , freq )

Negative log-likelihood for the Birnbaum-Saunders distribution.

nlogL = bisalike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the Birnbaum-Saunders
distribution with (1) scale parameter beta and (2) shape parameter
gamma given in the two-element vector params .

[ nlogL , acov ] = bisalike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = bisalike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = bisalike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

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

See also:
bisacdf,
bisainv,
bisapdf,
bisarnd,
bisafit,
bisastat


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Negative log-likelihood for the Birnbaum-Saunders distribution.



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burrfit


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statistics: paramhat = burrfit ( x )
statistics: [ paramhat , paramci ] = burrfit ( x )
statistics: [ paramhat , paramci ] = burrfit ( x , alpha )
statistics: [&hellip;] = burrfit ( x , alpha , censor )
statistics: [&hellip;] = burrfit ( x , alpha , censor , freq )
statistics: [&hellip;] = burrfit ( x , alpha , censor , freq , options )

Estimate mean and confidence intervals for the Burr type XII distribution.

muhat = burrfit ( x ) returns the maximum likelihood
estimates of the parameters of the Burr type XII distribution given the data
in x . paramhat (1) is the scale parameter, lambda ,
paramhat (2) is the first shape parameter, c , and
paramhat (3) is the second shape parameter, k

[ paramhat , paramci ] = burrfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = burrfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = burrfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = burrfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = burrfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute the maximum likelihood
estimates. options is a structure with the following field and its
default value:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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

See also:
burrcdf,
burrinv,
burrpdf,
burrrnd,
burrlike,
burrstat


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Estimate mean and confidence intervals for the Burr type XII distribution.



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burrlike


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statistics: nlogL = burrlike ( params , x )
statistics: [ nlogL , acov ] = burrlike ( params , x )
statistics: [&hellip;] = burrlike ( params , x , censor )
statistics: [&hellip;] = burrlike ( params , x , censor , freq )

Negative log-likelihood for the Burr type XII distribution.

nlogL = burrlike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the Burr type XII
distribution with (1) scale parameter lambda , (2) first shape parameter
c , and (3) second shape parameter k given in the three-element
vector params .

[ nlogL , acov ] = burrlike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances.

[&hellip;] = burrlike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = burrlike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

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

See also:
burrcdf,
burrinv,
burrpdf,
burrrnd,
burrfit,
burrstat


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Negative log-likelihood for the Burr type XII distribution.



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copulafit


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statistics: rho = copulafit ( "Gaussian" , u )
statistics: [ rho , nu ] = copulafit ( "t" , u )
statistics: [ param , ci ] = copulafit ( family , u )
statistics: [&hellip;] = copulafit (&hellip;, "alpha" , a )

Fit a copula to data.

copulafit ( family , u ) returns the maximum-likelihood
estimate of the parameter of a copula of the family family , fit to the
data in u . The rows of u are observations and its columns are
variables; all entries must lie strictly inside the unit interval
(0,1) , as produced for example by a probability-integral transform or
by ecdf / ksdensity .

family is the copula family name. It can be "Gaussian" for the
Gaussian family, "t" for the Student&rsquo;s t family, "Clayton"
for the Clayton family, "Gumbel" for the Gumbel-Hougaard family, or
"Frank" for the Frank family.

The returned value depends on the family:

For "Gaussian" , rho = copulafit ("Gaussian",
u ) returns the estimated linear correlation matrix rho , computed
as the sample correlation of the normal scores norminv ( u ) . The
data may have two or more columns.
For "t" , copulafit ("t", u ) returns the estimated
correlation matrix rho and the degrees of freedom nu as
[ rho , nu ] , obtained by maximizing the copula
log-likelihood. Only bivariate data (two columns) are supported.
For the Archimedean families "Clayton" , "Gumbel" , and
"Frank" , [ param , ci ] = copulafit ( family ,
u ) returns the scalar copula parameter param and, optionally, a
two-element vector ci with the lower and upper confidence bounds. Only
bivariate data are supported.

copulafit (&hellip;, "alpha" , a ) sets the significance
level for the confidence interval to a , so that ci has coverage
100 * (1 - a ) percent. The default is a = 0.05 .
The confidence interval is a Wald interval whose standard error is obtained
from the outer-product-of-gradients estimate of the information.

See also:
copulastat,
copulaparam,
copulacdf,
copulapdf,
copularnd


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Fit a copula to data.



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evfit


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statistics: paramhat = evfit ( x )
statistics: [ paramhat , paramci ] = evfit ( x )
statistics: [ paramhat , paramci ] = evfit ( x , alpha )
statistics: [&hellip;] = evfit ( x , alpha , censor )
statistics: [&hellip;] = evfit ( x , alpha , censor , freq )
statistics: [&hellip;] = evfit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for the extreme value
distribution.

paramhat = evfit ( x ) returns the maximum likelihood
estimates of the parameters of the extreme value distribution (also known as
the Gumbel or the type I generalized extreme value distribution) given the
data in x . paramhat (1) is the location parameter,
mu , and paramhat (2) is the scale parameter, sigma .

[ paramhat , paramci ] = evfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = evfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = evfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = evfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = evfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute the maximum likelihood
estimates. options is a structure with the following field and its
default value:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

The Gumbel distribution is used to model the distribution of the maximum (or
the minimum) of a number of samples of various distributions. This version
is suitable for modeling minima. For modeling maxima, use the alternative
Gumbel fitting function, gumbelfit .

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

See also:
evcdf,
evinv,
evpdf,
evrnd,
evlike,
evstat,
gumbelfit


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Estimate parameters and confidence intervals for the extreme value distribution.



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evlike


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statistics: nlogL = evlike ( params , x )
statistics: [ nlogL , acov ] = evlike ( params , x )
statistics: [&hellip;] = evlike ( params , x , censor )
statistics: [&hellip;] = evlike ( params , x , censor , freq )

Negative log-likelihood for the extreme value distribution.

nlogL = evlike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the extreme value
distribution (also known as the Gumbel or the type I generalized extreme
value distribution) with (1) location parameter mu and (2) scale
parameter sigma given in the two-element vector params .

[ nlogL , acov ] = evlike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances.

[&hellip;] = evlike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = evlike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

The Gumbel distribution is used to model the distribution of the maximum (or
the minimum) of a number of samples of various distributions. This version
is suitable for modeling minima. For modeling maxima, use the alternative
Gumbel likelihood function, gumbellike .

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

See also:
evcdf,
evinv,
evpdf,
evrnd,
evfit,
evstat,
gumbellike


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Negative log-likelihood for the extreme value distribution.



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# length: 6
expfit


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statistics: muhat = expfit ( x )
statistics: [ muhat , muci ] = expfit ( x )
statistics: [ muhat , muci ] = expfit ( x , alpha )
statistics: [&hellip;] = expfit ( x , alpha , censor )
statistics: [&hellip;] = expfit ( x , alpha , censor , freq )

Estimate mean and confidence intervals for the exponential distribution.

muhat = expfit ( x ) returns the maximum likelihood estimate
of the mean parameter, muhat , of the exponential distribution given the
data in x . x is expected to be a non-negative vector. If x
is an array, the mean will be computed for each column of x . If any
elements of x are NaN, that vector&rsquo;s mean will be returned as NaN.

[ muhat , muci ] = expfit ( x ) returns the 95%
confidence intervals for the parameter estimate. If x is a vector,
muci is a two element column vector. If x is an array, each
column of data will have a confidence interval returned as a two-row array.

[&hellip;] = evfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values. Any invalid values for alpha
will return NaN for both CI bounds.

[&hellip;] = expfit ( x , alpha , censor ) accepts a
logical or numeric array, censor , of the same size as x with
1 s for observations that are right-censored and 0 s for
observations that are observed exactly. Any non-zero elements are regarded
as 1 s. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = expfit ( x , alpha , censor , freq )
accepts a frequency array, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

Matlab incompatibility: Matlab&rsquo;s expfit produces unpredictable results
for some cases with higher dimensions (specifically 1 x m x n x ... arrays).
Octave&rsquo;s implementation allows for n&times;D arrays, consistently performing
calculations on individual column vectors. Additionally, censor and
freq can be used with arrays of any size, whereas Matlab only allows
their use when x is a vector.

A common alternative parameterization of the exponential distribution is to
use the parameter λ defined as the mean number of events in an
interval as opposed to the parameter μ , which is the mean wait time
for an event to occur. λ and μ are reciprocals,
i.e. μ = 1 / λ .

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

See also:
expcdf,
expinv,
explpdf,
exprnd,
explike,
expstat


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# length: 72
Estimate mean and confidence intervals for the exponential distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
explike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1724
statistics: nlogL = explike ( mu , x )
statistics: [ nlogL , avar ] = explike ( mu , x )
statistics: [&hellip;] = explike ( mu , x , censor )
statistics: [&hellip;] = explike ( mu , x , censor , freq )

Negative log-likelihood for the exponential distribution.

nlogL = explike ( mu , x ) returns the negative
log likelihood of the data in x corresponding to the exponential
distribution with mean parameter mu . x must be a vector of
non-negative values, otherwise NaN is returned.

[ nlogL , avar ] = explike ( mu , x ) also
returns the inverse of Fisher&rsquo;s information matrix, avar . If the input
mean parameter, mu , is the maximum likelihood estimate, avar is
its asymptotic variance.

[&hellip;] = explike ( mu , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = explike ( mu , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

A common alternative parameterization of the exponential distribution is to
use the parameter λ defined as the mean number of events in an
interval as opposed to the parameter μ , which is the mean wait time
for an event to occur. λ and μ are reciprocals,
i.e. μ = 1 / λ .

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

See also:
expcdf,
expinv,
exppdf,
exprnd,
expfit,
expstat


# name: <cell-element>
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# elements: 1
# length: 57
Negative log-likelihood for the exponential distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
gamfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2445
statistics: paramhat = gamfit ( x )
statistics: [ paramhat , paramci ] = gamfit ( x )
statistics: [ paramhat , paramci ] = gamfit ( x , alpha )
statistics: [&hellip;] = gamfit ( x , alpha , censor )
statistics: [&hellip;] = gamfit ( x , alpha , censor , freq )
statistics: [&hellip;] = gamfit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for the Gamma distribution.

paramhat = gamfit ( x ) returns the maximum likelihood
estimates of the parameters of the Gamma distribution given the data in
x . paramhat (1) is the shape parameter, a , and
paramhat (2) is the scale parameter, b .

[ paramhat , paramci ] = gamfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = gamfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = gamfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = gamfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = gamfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute the maximum likelihood
estimates. options is a structure with the following field and its
default value:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

OCTAVE/MATLAB use the alternative parameterization given by the pair
α, β , i.e. shape a and scale b . In Wikipedia, the two
common parameterizations use the pairs k, θ , as shape and scale, and
α, β , as shape and rate, respectively. The parameter names a
and b used here (for MATLAB compatibility) correspond to the parameter
notation k, θ instead of the α, β as reported in Wikipedia.

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

See also:
gamcdf,
gampdf,
gaminv,
gamrnd,
gamlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 72
Estimate parameters and confidence intervals for the Gamma distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
gamlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1876
statistics: nlogL = gamlike ( params , x )
statistics: [ nlogL , acov ] = gamlike ( params , x )
statistics: [&hellip;] = gamlike ( params , x , censor )
statistics: [&hellip;] = gamlike ( params , x , censor , freq )

Negative log-likelihood for the Gamma distribution.

nlogL = gamlike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the Gamma distribution
with (1) shape parameter a and (2) scale parameter b given in the
two-element vector params .

[ nlogL , acov ] = gamlike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances.

[&hellip;] = gamlike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = gamlike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

OCTAVE/MATLAB use the alternative parameterization given by the pair
α, β , i.e. shape a and scale b . In Wikipedia, the two
common parameterizations use the pairs k, θ , as shape and scale, and
α, β , as shape and rate, respectively. The parameter names a
and b used here (for MATLAB compatibility) correspond to the parameter
notation k, θ instead of the α, β as reported in Wikipedia.

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

See also:
gamcdf,
gampdf,
gaminv,
gamrnd,
gamfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Negative log-likelihood for the Gamma distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
geofit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1288
statistics: pshat = geofit ( x )
statistics: [ pshat , psci ] = geofit ( x )
statistics: [ pshat , psci ] = geofit ( x , alpha )
statistics: [ pshat , psci ] = geofit ( x , alpha , freq )

Estimate parameter and confidence intervals for the geometric distribution.

pshat = geofit ( x ) returns the maximum likelihood estimate
(MLE) of the probability of success for the geometric distribution. x
must be a vector.

[ pshat , psci ] = geofit ( x , alpha ) also returns
the 100 * (1 - alpha ) percent confidence intervals of the
estimated parameter. By default, the optional argument alpha is 0.05
corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = geofit ( x , alpha , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) .

The geometric distribution models the number of failures ( x ) of a
Bernoulli trial with probability ps before the first success.

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

See also:
geocdf,
geoinv,
geopdf,
geornd,
geostat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 75
Estimate parameter and confidence intervals for the geometric distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
gevfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2576
statistics: paramhat = gevfit ( x )
statistics: [ paramhat , paramci ] = gevfit ( x )
statistics: [ paramhat , paramci ] = gevfit ( x , alpha )
statistics: [ paramhat , paramci ] = gevfit ( x , alpha , freq )
statistics: [ paramhat , paramci ] = gevfit ( x , alpha , options )
statistics: [ paramhat , paramci ] = gevfit ( x , alpha , freq , options )

Estimate parameters and confidence intervals for the generalized extreme
value (GEV) distribution.

paramhat = gevfit ( x ) returns the maximum likelihood
estimates of the parameters of the GEV distribution given the data in
x . paramhat (1) is the shape parameter, k , and
paramhat (2) is the scale parameter, sigma , and
paramhat (3) is the location parameter, mu .

[ paramhat , paramci ] = gevfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = gevfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = gevfit ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

[ paramhat , paramci ] = gevfit ( x , alpha ,
options ) specifies control parameters for the iterative algorithm used
to compute ML estimates with the fminsearch function. options
is a structure with the following fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

When k < 0 , the GEV is the type III extreme value distribution.
When k > 0 , the GEV distribution is the type II, or Frechet,
extreme value distribution. If W has a Weibull distribution as
computed by the wblcdf function, then - W has a type III
extreme value distribution and 1/ W has a type II extreme value
distribution. In the limit as k approaches 0 , the GEV is the
mirror image of the type I extreme value distribution as computed by the
evcdf function.

The mean of the GEV distribution is not finite when k >= 1 , and
the variance is not finite when k >= 1/2 . The GEV distribution
has positive density only for values of x such that
k * ( x - mu ) / sigma > -1 .

Further information about the generalized extreme value distribution can be
found at
https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution

See also:
gevcdf,
gevinv,
gevpdf,
gevrnd,
gevlike,
gevstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 98
Estimate parameters and confidence intervals for the generalized extreme value (GEV) distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
gevfit_lmom


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 942
statistics: [ paramhat , paramci ] = gevfit_lmom ( data )

Find an estimator ( paramhat ) of the generalized extreme value (GEV)
distribution fitting data using the method of L-moments.

Arguments

data is the vector of given values.

Return values

paramhat is the 3-parameter maximum-likelihood parameter vector
[ k ; sigma ; mu ], where k is the shape parameter of the
GEV distribution, sigma is the scale parameter of the GEV distribution,
and mu is the location parameter of the GEV distribution.

paramci has the approximate 95% confidence intervals of the parameter
values (currently not implemented).

Examples

data = gevrnd (0.1, 1, 0, 100, 1);
[pfit, pci] = gevfit_lmom (data);
p1 = gevcdf (data,pfit(1),pfit(2),pfit(3));
[f, x] = ecdf (data);
plot(data, p1, 's', x, f)

References

Ailliot, P.; Thompson, C. & Thomson, P. Mixed methods for fitting the GEV
distribution, Water Resources Research, 2011, 47, W05551

See also:
gevfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 124
Find an estimator (paramhat) of the generalized extreme value (GEV) distribution fitting data using the method of L-moments.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
gevlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2391
statistics: nlogL = gevlike ( params , x )
statistics: [ nlogL , acov ] = gevlike ( params , x )
statistics: [ nlogL , acov ] = gevlike ( params , x , freq )

Negative log-likelihood for the generalized extreme value (GEV) distribution.

nlogL = gevlike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the GEV distribution
with (1) shape parameter k , (2) scale parameter sigma , and (3)
location parameter mu given in the three-element vector params .

[ nlogL , acov ] = gevlike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances.

[&hellip;] = gevlike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

When k < 0 , the GEV is the type III extreme value distribution.
When k > 0 , the GEV distribution is the type II, or Frechet,
extreme value distribution. If W has a Weibull distribution as
computed by the wblcdf function, then - W has a type III
extreme value distribution and 1/ W has a type II extreme value
distribution. In the limit as k approaches 0 , the GEV is the
mirror image of the type I extreme value distribution as computed by the
evcdf function.

MATLAB compatibility. At exactly k = 0 the returned
ACOV deviates from MATLAB&rsquo;s deliberately. Both implementations agree
to thirteen digits for any k != 0 , and both their
k != 0 expressions converge on the values returned here as
k approaches 0 ; MATLAB&rsquo;s own k = 0 branch
returns something else entirely, which its k != 0 branch
therefore contradicts. The Gumbel-limit expressions used here are the
limits of the general ones, so ACOV is continuous at 0 . This
is independent of the sample size.

The mean of the GEV distribution is not finite when k >= 1 , and
the variance is not finite when k >= 1/2 . The GEV distribution
has positive density only for values of x such that
k * ( x - mu ) / sigma > -1 .

Further information about the generalized extreme value distribution can be
found at
https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution

See also:
gevcdf,
gevinv,
gevpdf,
gevrnd,
gevfit,
gevstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 77
Negative log-likelihood for the generalized extreme value (GEV) distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
gpfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3224
statistics: paramhat = gpfit ( x )
statistics: [ paramhat , paramci ] = gpfit ( x )
statistics: [ paramhat , paramci ] = gpfit ( x , alpha )
statistics: [ paramhat , paramci ] = gpfit ( x , alpha , options )
statistics: [ paramhat , paramci ] = gpfit ( x , alpha , options , freq )

Estimate parameters and confidence intervals for the generalized Pareto
distribution.

paramhat = gpfit ( x ) returns the maximum likelihood
estimates of the parameters of the generalized Pareto distribution given the
data in x . paramhat (1) is the shape parameter, k ,
and paramhat (2) is the scale parameter, sigma .

gpfit does not estimate the location parameter theta and assumes
it to be zero, so x must not contain negative values. To fit data with
a known nonzero theta , subtract it from x before calling
gpfit ; the estimates of k and sigma are unchanged by the
shift.

[ paramhat , paramci ] = gpfit ( x ) returns the 95%
confidence intervals for the estimated parameters k and sigma as
a 2 -by- 2 matrix whose first row holds the lower bounds and
whose second row holds the upper bounds.

[&hellip;] = gpfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = gpfit ( x , alpha , options )
specifies control parameters for the iterative algorithm used to compute ML
estimates with the fminsearch function. options is a structure
with the following fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

[&hellip;] = gpfit ( x , alpha , options , freq )
accepts a vector of the same size as x giving the number of times each
element of x was observed. This fourth argument is an Octave
extension; MATLAB&rsquo;s gpfit takes three inputs at most.

When the shape parameter falls below -1 the likelihood is unbounded:
the density at the upper endpoint of the support diverges as that endpoint
closes onto the largest observation, so no maximum likelihood estimate
exists and whatever is returned is an arbitrary point on that ridge.
gpfit warns in this case and returns NaN confidence intervals.
The estimate it does return always keeps every observation strictly inside
the fitted support, since the likelihood is infinite outside it. This is a
deliberate deviation: MATLAB has been measured returning parameters for such
data under which the largest observation has zero density and its own
gplike returns Inf .

When k = 0 and theta = 0 , the Generalized Pareto
is equivalent to the exponential distribution. When k > 0 and
theta = k / k the Generalized Pareto is equivalent
to the Pareto distribution. The mean of the Generalized Pareto is not finite
when k >= 1 and the variance is not finite when
k >= 1/2 . When k >= 0 , the Generalized Pareto
has positive density for x > theta , or, when
theta < 0 , for
0 <= ( x - theta ) / sigma <= -1 / k .

Further information about the generalized Pareto distribution can be found at
https://en.wikipedia.org/wiki/Generalized_Pareto_distribution

See also:
gpcdf,
gpinv,
gppdf,
gprnd,
gplike,
gpstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 85
Estimate parameters and confidence intervals for the generalized Pareto distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
gplike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1966
statistics: nlogL = gplike ( params , x )
statistics: [ nlogL , acov ] = gplike ( params , x )
statistics: [&hellip;] = gplike ( params , x , freq )

Negative log-likelihood for the generalized Pareto distribution.

nlogL = gplike ( params , x ) returns the negative
log-likelihood of the data in x corresponding to the generalized Pareto
distribution with (1) shape parameter k and (2) scale parameter
sigma given in the two-element vector params .

gplike does not accept a location parameter theta and assumes it
to be zero. If the location is known to be nonzero, subtract it from
x before calling gplike .

[ nlogL , acov ] = gplike ( params , x ) returns
the inverse of Fisher&rsquo;s information matrix, acov , a
2 -by- 2 matrix. If the input parameter values in params
are the maximum likelihood estimates, the diagonal elements of acov are
their asymptotic variances. acov is based on the observed Fisher&rsquo;s
information, not the expected information.

[&hellip;] = gplike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) . This third
argument is an Octave extension; MATLAB&rsquo;s gplike takes two inputs.

When k = 0 and mu = 0 , the Generalized Pareto CDF
is equivalent to the exponential distribution. When k > 0 and
mu = k / k the Generalized Pareto is equivalent to
the Pareto distribution. The mean of the Generalized Pareto is not finite
when k >= 1 and the variance is not finite when
k >= 1/2 . When k >= 0 , the Generalized Pareto
has positive density for x > mu , or, when
mu < 0 , for
0 <= ( x - mu ) / sigma <= -1 / k .

Further information about the generalized Pareto distribution can be found at
https://en.wikipedia.org/wiki/Generalized_Pareto_distribution

See also:
gpcdf,
gpinv,
gppdf,
gprnd,
gpfit,
gpstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Negative log-likelihood for the generalized Pareto distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
gumbelfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2470
statistics: paramhat = gumbelfit ( x )
statistics: [ paramhat , paramci ] = gumbelfit ( x )
statistics: [ paramhat , paramci ] = gumbelfit ( x , alpha )
statistics: [&hellip;] = gumbelfit ( x , alpha , censor )
statistics: [&hellip;] = gumbelfit ( x , alpha , censor , freq )
statistics: [&hellip;] = gumbelfit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for Gumbel distribution.

paramhat = gumbelfit ( x ) returns the maximum likelihood
estimates of the parameters of the Gumbel distribution (also known as
the extreme value or the type I generalized extreme value distribution) given
in x . paramhat (1) is the location parameter, mu ,
and paramhat (2) is the scale parameter, beta .

[ paramhat , paramci ] = gumbelfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = gumbelfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = gumbelfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = gumbelfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = gumbelfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute the maximum likelihood
estimates. options is a structure with the following field and its
default value:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

The Gumbel distribution is used to model the distribution of the maximum (or
the minimum) of a number of samples of various distributions. This version
is suitable for modeling maxima. For modeling minima, use the alternative
extreme value fitting function, evfit .

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

See also:
gumbelcdf,
gumbelinv,
gumbelpdf,
gumbelrnd,
gumbellike,
gumbelstat,
evfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 69
Estimate parameters and confidence intervals for Gumbel distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
gumbellike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1914
statistics: nlogL = gumbellike ( params , x )
statistics: [ nlogL , avar ] = gumbellike ( params , x )
statistics: [&hellip;] = gumbellike ( params , x , censor )
statistics: [&hellip;] = gumbellike ( params , x , censor , freq )

Negative log-likelihood for the extreme value distribution.

nlogL = gumbellike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the Gumbel
distribution (also known as the extreme value or the type I generalized
extreme value distribution) with (1) location parameter mu and (2)
scale parameter beta given in the two-element vector params .

[ nlogL , acov ] = gumbellike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances.

[&hellip;] = gumbellike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = gumbellike ( params , x , censor ,
freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

The Gumbel distribution is used to model the distribution of the maximum (or
the minimum) of a number of samples of various distributions. This version
is suitable for modeling maxima. For modeling minima, use the alternative
extreme value likelihood function, evlike .

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

See also:
gumbelcdf,
gumbelinv,
gumbelpdf,
gumbelrnd,
gumbelfit,
gumbelstat,
evlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
Negative log-likelihood for the extreme value distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5
hnfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1646
statistics: [ paramhat , paramci ] = hnfit ( x , mu )
statistics: [ paramhat , paramci ] = hnfit ( x , mu , alpha )
statistics: [ paramhat , paramci ] = hnfit ( x , mu , alpha , freq )

Estimate parameters and confidence intervals for the half-normal
distribution.

paramhat = hnfit ( x , mu ) returns the maximum
likelihood estimates of the parameters of the half-normal distribution given
the data in vector x and the location parameter mu .
paramhat (1) is the location parameter, mu , and
paramhat (2) is the scale parameter, sigma . Although
mu is returned in the estimated paramhat , hnfit does not
estimate the location parameter mu , and it must be assumed to be known,
given as a fixed parameter in input argument mu .

[ paramhat , paramci ] = hnfit ( x , mu ) returns
the 95% confidence intervals for the estimated scale parameter sigma .
The first column of paramci includes the location parameter mu
without any confidence bounds.

[&hellip;] = hnfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals of the estimated
scale parameter. By default, the optional argument alpha is 0.05
corresponding to 95% confidence intervals.

[&hellip;] = hnfit ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

The half-normal CDF is only defined for x >= mu .

Further information about the half-normal distribution can be found at
https://en.wikipedia.org/wiki/Half-normal_distribution

See also:
hncdf,
hninv,
hnpdf,
hnrnd,
hnlike,
hnstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 78
Estimate parameters and confidence intervals for the half-normal distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
hnlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1220
statistics: nlogL = hnlike ( params , x )
statistics: [ nlogL , acov ] = hnlike ( params , x )
statistics: [ nlogL , acov ] = hnlike ( params , x , freq )

Negative log-likelihood for the half-normal distribution.

nlogL = hnlike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the half-normal
distribution with (1) location parameter mu and (2) scale parameter
sigma given in the two-element vector params .

[ nlogL , acov ] = hnlike ( params , x ) returns
the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances.

[&hellip;] = hnlike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) .

The half-normal CDF is only defined for x >= mu .

Further information about the half-normal distribution can be found at
https://en.wikipedia.org/wiki/Half-normal_distribution

See also:
hncdf,
hninv,
hnpdf,
hnrnd,
hnfit,
hnstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
Negative log-likelihood for the half-normal distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
invgfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2127
statistics: paramhat = invgfit ( x )
statistics: [ paramhat , paramci ] = invgfit ( x )
statistics: [ paramhat , paramci ] = invgfit ( x , alpha )
statistics: [&hellip;] = invgfit ( x , alpha , censor )
statistics: [&hellip;] = invgfit ( x , alpha , censor , freq )
statistics: [&hellip;] = invgfit ( x , alpha , censor , freq , options )

Estimate mean and confidence intervals for the inverse Gaussian distribution.

mu0 = invgfit ( x ) returns the maximum likelihood
estimates of the parameters of the inverse Gaussian distribution given the
data in x . paramhat (1) is the scale parameter, mu ,
and paramhat (2) is the shape parameter, lambda .

[ paramhat , paramci ] = invgfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = invgfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = invgfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = invgfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = invgfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute ML estimates with the
fminsearch function. options is a structure with the following
fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

Further information about the inverse Gaussian distribution can be found at
https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution

See also:
invgcdf,
invginv,
invgpdf,
invgrnd,
invglike,
invgstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 77
Estimate mean and confidence intervals for the inverse Gaussian distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
invglike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1554
statistics: nlogL = invglike ( params , x )
statistics: [ nlogL , acov ] = invglike ( params , x )
statistics: [&hellip;] = invglike ( params , x , censor )
statistics: [&hellip;] = invglike ( params , x , censor , freq )

Negative log-likelihood for the inverse Gaussian distribution.

nlogL = invglike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the inverse Gaussian
distribution with (1) scale parameter mu and (2) shape parameter
lambda given in the two-element vector params .

[ nlogL , acov ] = invglike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = invglike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = invglike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

Further information about the inverse Gaussian distribution can be found at
https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution

See also:
invgcdf,
invginv,
invgpdf,
invgrnd,
invgfit,
invgstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Negative log-likelihood for the inverse Gaussian distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
logifit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2090
statistics: paramhat = logifit ( x )
statistics: [ paramhat , paramci ] = logifit ( x )
statistics: [ paramhat , paramci ] = logifit ( x , alpha )
statistics: [&hellip;] = logifit ( x , alpha , censor )
statistics: [&hellip;] = logifit ( x , alpha , censor , freq )
statistics: [&hellip;] = logifit ( x , alpha , censor , freq , options )

Estimate mean and confidence intervals for the logistic distribution.

mu0 = logifit ( x ) returns the maximum likelihood
estimates of the parameters of the logistic distribution given the data in
x . paramhat (1) is the scale parameter, mu , and
paramhat (2) is the shape parameter, s .

[ paramhat , paramci ] = logifit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = logifit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = logifit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = logifit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = logifit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute ML estimates with the
fminsearch function. options is a structure with the following
fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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

See also:
logicdf,
logiinv,
logipdf,
logirnd,
logilike,
logistat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 69
Estimate mean and confidence intervals for the logistic distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
logilike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1524
statistics: nlogL = logilike ( params , x )
statistics: [ nlogL , acov ] = logilike ( params , x )
statistics: [&hellip;] = logilike ( params , x , censor )
statistics: [&hellip;] = logilike ( params , x , censor , freq )

Negative log-likelihood for the logistic distribution.

nlogL = logilike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the logistic
distribution with (1) location parameter mu and (2) scale parameter
sigma given in the two-element vector params .

[ nlogL , acov ] = logilike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = logilike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = logilike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

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

See also:
logicdf,
logiinv,
logipdf,
logirnd,
logifit,
logistat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
Negative log-likelihood for the logistic distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
loglfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2356
statistics: paramhat = loglfit ( x )
statistics: [ paramhat , paramci ] = loglfit ( x )
statistics: [ paramhat , paramci ] = loglfit ( x , alpha )
statistics: [&hellip;] = loglfit ( x , alpha , censor )
statistics: [&hellip;] = loglfit ( x , alpha , censor , freq )
statistics: [&hellip;] = loglfit ( x , alpha , censor , freq , options )

Estimate mean and confidence intervals for the log-logistic distribution.

mu0 = loglfit ( x ) returns the maximum likelihood
estimates of the parameters of the log-logistic distribution given the data
in x . paramhat (1) is the mean parameter, mu , and
paramhat (2) is the scale parameter, sigma .

[ paramhat , paramci ] = loglfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = loglfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = loglfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = loglfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = loglfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute ML estimates with the
fminsearch function. options is a structure with the following
fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

Further information about the loglogistic distribution can be found at
https://en.wikipedia.org/wiki/Log-logistic_distribution

OCTAVE/MATLAB use an alternative parameterization given by the pair
μ, σ , i.e. mu and sigma , in analogy with the logistic
distribution. Their relation to the α and b parameters used
in Wikipedia are given below:

mu = log ( a )
sigma = 1 / a

See also:
loglcdf,
loglinv,
loglpdf,
loglrnd,
logllike,
loglstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Estimate mean and confidence intervals for the log-logistic distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
logllike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1779
statistics: nlogL = logllike ( params , x )
statistics: [ nlogL , acov ] = logllike ( params , x )
statistics: [&hellip;] = logllike ( params , x , censor )
statistics: [&hellip;] = logllike ( params , x , censor , freq )

Negative log-likelihood for the log-logistic distribution.

nlogL = logllike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the log-logistic
distribution with (1) scale parameter a and (2) shape parameter b
given in the two-element vector params .

[ nlogL , acov ] = logllike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = logllike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = logllike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

Further information about the loglogistic distribution can be found at
https://en.wikipedia.org/wiki/Log-logistic_distribution

OCTAVE/MATLAB use an alternative parameterization given by the pair
μ, σ , i.e. mu and sigma , in analogy with the logistic
distribution. Their relation to the α and b parameters used
in Wikipedia are given below:

mu = log ( a )
sigma = 1 / a

See also:
loglcdf,
loglinv,
loglpdf,
loglrnd,
loglfit,
loglstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
Negative log-likelihood for the log-logistic distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
lognfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2488
statistics: paramhat = lognfit ( x )
statistics: [ paramhat , paramci ] = lognfit ( x )
statistics: [ paramhat , paramci ] = lognfit ( x , alpha )
statistics: [&hellip;] = lognfit ( x , alpha , censor )
statistics: [&hellip;] = lognfit ( x , alpha , censor , freq )
statistics: [&hellip;] = lognfit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for the lognormal distribution.

paramhat = lognfit ( x ) returns the maximum likelihood
estimates of the parameters of the lognormal distribution given the data in
vector x . paramhat ([1, 2]) corresponds to the mean and
standard deviation, respectively, of the associated normal distribution.

If a random variable follows this distribution, its logarithm is normally
distributed with mean mu and standard deviation sigma .

[ paramhat , paramci ] = lognfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = lognfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = lognfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = lognfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = lognfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute ML estimates with the
fminsearch function. options is a structure with the following
fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

With no censor, the estimate of the standard deviation,
paramhat (2) , is the square root of the unbiased estimate of the
variance of log ( x ) . With censored data, the maximum
likelihood estimate is returned.

Further information about the lognormal distribution can be found at
https://en.wikipedia.org/wiki/Log-normal_distribution

See also:
logncdf,
logninv,
lognpdf,
lognrnd,
lognlike,
lognstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 76
Estimate parameters and confidence intervals for the lognormal distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
lognlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1920
statistics: nlogL = lognlike ( params , x )
statistics: [ nlogL , avar ] = lognlike ( params , x )
statistics: [&hellip;] = lognlike ( params , x , censor )
statistics: [&hellip;] = lognlike ( params , x , censor , freq )

Negative log-likelihood for the lognormal distribution.

nlogL = lognlike ( params , x ) returns the negative
log-likelihood of the data in x corresponding to the lognormal
distribution with (1) location parameter mu and (2) scale parameter
sigma given in the two-element vector params , which correspond to
the mean and standard deviation of the associated normal distribution.
Missing values, NaNs , are ignored. Negative values of x are
treated as missing values.

If a random variable follows this distribution, its logarithm is normally
distributed with mean mu and standard deviation sigma .

[ nlogL , avar ] = lognlike ( params , x )
returns the inverse of Fisher&rsquo;s information matrix, avar . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of avar are their asymptotic variances. avar
is based on the observed Fisher&rsquo;s information, not the expected information.

[&hellip;] = lognlike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = lognlike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

Further information about the lognormal distribution can be found at
https://en.wikipedia.org/wiki/Log-normal_distribution

See also:
logncdf,
logninv,
lognpdf,
lognrnd,
lognfit,
lognstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
Negative log-likelihood for the lognormal distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
nakafit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2047
statistics: paramhat = nakafit ( x )
statistics: [ paramhat , paramci ] = nakafit ( x )
statistics: [ paramhat , paramci ] = nakafit ( x , alpha )
statistics: [&hellip;] = nakafit ( x , alpha , censor )
statistics: [&hellip;] = nakafit ( x , alpha , censor , freq )
statistics: [&hellip;] = nakafit ( x , alpha , censor , freq , options )

Estimate mean and confidence intervals for the Nakagami distribution.

mu0 = nakafit ( x ) returns the maximum likelihood
estimates of the parameters of the Nakagami distribution given the data in
x . paramhat (1) is the shape parameter, mu , and
paramhat (2) is the spread parameter, omega .

[ paramhat , paramci ] = nakafit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = nakafit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = nakafit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = nakafit ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq must contain non-negative integer frequencies for the
corresponding elements in x . By default, or if left empty,
freq = ones (size ( x )) .

[&hellip;] = nakafit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute ML estimates with the
fminsearch function. options is a structure with the following
fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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

See also:
nakacdf,
nakainv,
nakapdf,
nakarnd,
nakalike,
nakastat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 69
Estimate mean and confidence intervals for the Nakagami distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nakalike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1473
statistics: nlogL = nakalike ( params , x )
statistics: [ nlogL , acov ] = nakalike ( params , x )
statistics: [&hellip;] = nakalike ( params , x , censor )
statistics: [&hellip;] = nakalike ( params , x , censor , freq )

Negative log-likelihood for the Nakagami distribution.

nlogL = nakalike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the Nakagami
distribution with (1) shape parameter mu and (2) spread parameter
omega given in the two-element vector params .

[ nlogL , acov ] = nakalike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = nakalike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = nakalike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq must contain non-negative integer frequencies for the
corresponding elements in x . By default, or if left empty,
freq = ones (size ( x )) .

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

See also:
nakacdf,
nakainv,
nakapdf,
nakarnd,
nakafit,
nakastat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
Negative log-likelihood for the Nakagami distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
nbinfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2988
statistics: paramhat = nbinfit ( x )
statistics: [ paramhat , paramci ] = nbinfit ( x )
statistics: [ paramhat , paramci ] = nbinfit ( x , alpha )
statistics: [ paramhat , paramci ] = nbinfit ( x , alpha , freq )
statistics: [ paramhat , paramci ] = nbinfit ( x , alpha , options )
statistics: [ paramhat , paramci ] = nbinfit ( x , alpha , freq , options )

Estimate parameter and confidence intervals for the negative binomial
distribution.

paramhat = nbinfit ( x ) returns the maximum likelihood
estimates of the parameters of the negative binomial distribution given the
data in vector x . paramhat (1) is the number of successes
until the experiment is stopped, r , and paramhat (2) is
the probability of success in each experiment, ps .

[ paramhat , paramci ] = nbinfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[ paramhat , paramci ] = nbinfit ( x , alpha ) also
returns the 100 * (1 - alpha ) percent confidence intervals of
the estimated parameter. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals.

[&hellip;] = nbinlike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

[ paramhat , paramci ] = nbinfit ( x , alpha ,
options ) specifies control parameters for the iterative algorithm used
to compute ML estimates with the fminsearch function. options
is a structure with the following fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

When r is an integer, the negative binomial distribution is also known
as the Pascal distribution and it models the number of failures in x
before a specified number of successes is reached in a series of independent,
identical trials. Its parameters are the probability of success in a single
trial, ps , and the number of successes, r . A special case of the
negative binomial distribution, when r = 1 , is the geometric
distribution, which models the number of failures before the first success.

r can also have non-integer positive values, in which form the negative
binomial distribution, also known as the Polya distribution, has no
interpretation in terms of repeated trials, but, like the Poisson
distribution, it is useful in modeling count data. The negative binomial
distribution is more general than the Poisson distribution because it has a
variance that is greater than its mean, making it suitable for count data
that do not meet the assumptions of the Poisson distribution. In the limit,
as r increases to infinity, the negative binomial distribution
approaches the Poisson distribution.

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

See also:
nbincdf,
nbininv,
nbinpdf,
nbinrnd,
nbinlike,
nbinstat


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Estimate parameter and confidence intervals for the negative binomial distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
nbinlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2393
statistics: nlogL = nbinlike ( params , x )
statistics: [ nlogL , avar ] = nbinlike ( params , x )
statistics: [ nlogL , avar ] = nbinlike ( params , x , freq )

Negative log-likelihood for the negative binomial distribution.

nlogL = nbinlike ( params , x ) returns the negative
log likelihood of the negative binomial distribution with (1) parameter
r and (2) parameter ps , given in the two-element vector
params , where r is the number of successes until the experiment
is stopped and ps is the probability of success in each experiment,
given the number of failures in x .

[ nlogL , avar ] = nbinlike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, avar . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = nbinlike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

When r is an integer, the negative binomial distribution is also known
as the Pascal distribution and it models the number of failures in x
before a specified number of successes is reached in a series of independent,
identical trials. Its parameters are the probability of success in a single
trial, ps , and the number of successes, r . A special case of the
negative binomial distribution, when r = 1 , is the geometric
distribution, which models the number of failures before the first success.

r can also have non-integer positive values, in which form the negative
binomial distribution, also known as the Polya distribution, has no
interpretation in terms of repeated trials, but, like the Poisson
distribution, it is useful in modeling count data. The negative binomial
distribution is more general than the Poisson distribution because it has a
variance that is greater than its mean, making it suitable for count data
that do not meet the assumptions of the Poisson distribution. In the limit,
as r increases to infinity, the negative binomial distribution
approaches the Poisson distribution.

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

See also:
nbincdf,
nbininv,
nbinpdf,
nbinrnd,
nbinfit,
nbinstat


# name: <cell-element>
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Negative log-likelihood for the negative binomial distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
normfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3291
statistics: muhat = normfit ( x )
statistics: [ muhat , sigmahat ] = normfit ( x )
statistics: [ muhat , sigmahat , muci ] = normfit ( x )
statistics: [ muhat , sigmahat , muci , sigmaci ] = normfit ( x )
statistics: [&hellip;] = normfit ( x , alpha )
statistics: [&hellip;] = normfit ( x , alpha , censor )
statistics: [&hellip;] = normfit ( x , alpha , censor , freq )
statistics: [&hellip;] = normfit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for the normal distribution.

[ muhat , sigmahat ] = normfit ( x ) estimates the
parameters of the normal distribution given the data in x . muhat
is an estimate of the mean, and sigmahat is an estimate of the standard
deviation.

[ muhat , sigmahat , muci , sigmaci ] = normfit
( x ) returns the 95% confidence intervals for the mean and standard
deviation estimates in the arrays muci and sigmaci , respectively.

x can be a vector or a matrix. When x is a matrix, the parameter
estimates and their confidence intervals are computed for each column. In
this case, normfit supports only 2 input arguments, x and
alpha . Optional arguments censor , freq , and options
can be used only when x is a vector.

alpha is a scalar value in the range (0,1) specifying the
confidence level for the confidence intervals calculated as
100&times;(1 - alpha)% . By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

censor is a logical vector of the same length as x specifying
whether each value in x is right-censored or not. 1 indicates
observations that are right-censored and 0 indicates observations that are
fully observed. With censoring, muhat and sigmahat are the
maximum likelihood estimates (MLEs). If empty, the default is an array of
0s, meaning that all observations are fully observed.

freq is a vector of the same length as x and it typically
contains non-negative integer counts of the corresponding elements in
x . If empty, the default is an array of 1s, meaning one observation
per element of x . To obtain the weighted MLEs for a data set with
censoring, specify weights of observations, normalized to the number of
observations in x . However, when there is no censored data (default),
the returned estimate for standard deviation is not exactly the WMLE. To
compute the weighted MLE, multiply the value returned in sigmahat by
sqrt ((sum ( freq ) - 1) / sum ( freq )) . The square root is
needed because the factor corrects a variance, while sigmahat is a
standard deviation. This correction is needed because normfit
normally computes sigmahat using an unbiased variance estimator when
there is no censored data. When there is censoring
in the data, the correction is not needed, since normfit does not use
the unbiased variance estimator in that case.

options is a structure with the control parameters for
fminsearch which is used internally to compute MLEs for censored data.
By default, it uses the following options:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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

See also:
normcdf,
norminv,
normpdf,
normrnd,
normlike,
normstat


# name: <cell-element>
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# elements: 1
# length: 73
Estimate parameters and confidence intervals for the normal distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
normlike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1484
statistics: nlogL = normlike ( params , x )
statistics: [ nlogL , avar ] = normlike ( params , x )
statistics: [&hellip;] = normlike ( params , x , censor )
statistics: [&hellip;] = normlike ( params , x , censor , freq )

Negative log-likelihood for the normal distribution.

nlogL = normlike ( params , x ) returns the negative
log-likelihood for the normal distribution, evaluated at parameters
params(1) = mean and params(2) = standard deviation, given
x . nlogL is a scalar.

[ nlogL , avar ] = normlike ( params , x )
returns the inverse of Fisher&rsquo;s information matrix, avar . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of avar are their asymptotic variances. avar
is based on the observed Fisher&rsquo;s information, not the expected information.

[&hellip;] = normlike ( params , x , censor ) accepts
a boolean vector of the same size as x that is 1 for observations
that are right-censored and 0 for observations that are observed exactly.

[&hellip;] = normlike ( params , x , censor ,
freq ) accepts a frequency vector of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it may contain any non-integer non-negative
values. Pass in [] for censor to use its default value.

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

See also:
normcdf,
norminv,
normpdf,
normrnd,
normfit,
normstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Negative log-likelihood for the normal distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
poissfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1304
statistics: lambdahat = poissfit ( x )
statistics: [ lambdahat , lambdaci ] = poissfit ( x )
statistics: [ lambdahat , lambdaci ] = poissfit ( x , alpha )
statistics: [ lambdahat , lambdaci ] = poissfit ( x , alpha , freq )

Estimate parameter and confidence intervals for the Poisson distribution.

lambdahat = poissfit ( x ) returns the maximum likelihood
estimate of the rate parameter, lambda , of the Poisson distribution
given the data in x . x must be a vector of non-negative values.

[ lambdahat , lambdaci ] = poissfit ( x ) returns the 95%
confidence intervals for the parameter estimate.

[ lambdahat , lambdaci ] = poissfit ( x , alpha )
also returns the 100 * (1 - alpha ) percent confidence intervals
of the estimated parameter. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = poissfit ( x , alpha , freq ) accepts a
frequency vector or matrix, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x . freq cannot contain negative values.

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

See also:
poisscdf,
poissinv,
poisspdf,
poissrnd,
poisslike,
poisstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Estimate parameter and confidence intervals for the Poisson distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
poisslike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1124
statistics: nlogL = poisslike ( lambda , x )
statistics: [ nlogL , avar ] = poisslike ( lambda , x )
statistics: [&hellip;] = poisslike ( lambda , x , freq )

Negative log-likelihood for the Poisson distribution.

nlogL = poisslike ( lambda , x ) returns the negative
log likelihood of the data in x corresponding to the Poisson
distribution with rate parameter lambda . x must be a vector of
non-negative values.

[ nlogL , avar ] = poisslike ( lambda , x ) also
returns the inverse of Fisher&rsquo;s information matrix, avar . If the input
rate parameter, lambda , is the maximum likelihood estimate, avar
is its asymptotic variance.

[&hellip;] = poisslike ( lambda , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) .

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

See also:
poisscdf,
poissinv,
poisspdf,
poissrnd,
poissfit,
poisstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
Negative log-likelihood for the Poisson distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
raylfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1698
statistics: sigmaA = raylfit ( x )
statistics: [ sigmaA , sigmaci ] = raylfit ( x )
statistics: [ sigmaA , sigmaci ] = raylfit ( x , alpha )
statistics: [ sigmaA , sigmaci ] = raylfit ( x , alpha , censor )
statistics: [ sigmaA , sigmaci ] = raylfit ( x , alpha , censor , freq )

Estimate parameter and confidence intervals for the Rayleigh distribution.

sigmaA = raylfit ( x ) returns the maximum likelihood
estimate of the rate parameter, lambda , of the Rayleigh distribution
given the data in x . x must be a vector of non-negative values.

[ sigmaA , sigmaci ] = raylfit ( x ) returns the 95%
confidence intervals for the parameter estimate.

[ sigmaA , sigmaci ] = raylfit ( x , alpha )
also returns the 100 * (1 - alpha ) percent confidence intervals
of the estimated parameter. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = raylfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = raylfit ( x , alpha , censor , freq )
accepts a frequency vector or matrix, freq , of the same size as
x .
freq typically contains integer frequencies for the corresponding
elements in x . freq cannot contain negative values.

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

The prob.RayleighDistribution class names this same parameter
B , after MATLAB.

See also:
raylcdf,
raylinv,
raylpdf,
raylrnd,
rayllike,
raylstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 74
Estimate parameter and confidence intervals for the Rayleigh distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
rayllike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1190
statistics: nlogL = rayllike ( sigma , x )
statistics: [ nlogL , acov ] = rayllike ( sigma , x )
statistics: [&hellip;] = rayllike ( sigma , x , freq )

Negative log-likelihood for the Rayleigh distribution.

nlogL = rayllike ( sigma , x ) returns the negative
log likelihood of the data in x corresponding to the Rayleigh
distribution with rate parameter sigma . x must be a vector of
non-negative values.

[ nlogL , acov ] = rayllike ( sigma , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
rate parameter, sigma , is the maximum likelihood estimate, acov
is its asymptotic variance.

[&hellip;] = rayllike ( sigma , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) .

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

The prob.RayleighDistribution class names this same parameter
B , after MATLAB.

See also:
raylcdf,
raylinv,
raylpdf,
raylrnd,
raylfit,
raylstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
Negative log-likelihood for the Rayleigh distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
ricefit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2102
statistics: paramhat = ricefit ( x )
statistics: [ paramhat , paramci ] = ricefit ( x )
statistics: [ paramhat , paramci ] = ricefit ( x , alpha )
statistics: [&hellip;] = ricefit ( x , alpha , censor )
statistics: [&hellip;] = ricefit ( x , alpha , censor , freq )
statistics: [&hellip;] = ricefit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for the Rician distribution.

paramhat = ricefit ( x ) returns the maximum likelihood
estimates of the parameters of the Rician distribution given the data in
x . paramhat (1) is the non-centrality (distance)
parameter, s , and paramhat (2) is the scale parameter,
sigma .

[ paramhat , paramci ] = ricefit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = ricefit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = ricefit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = ricefit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = ricefit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute the maximum likelihood
estimates. options is a structure with the following field and its
default value:

options .Display = "off"
options .MaxFunEvals = 1000
options .MaxIter = 500
options .TolX = 1e-6

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

See also:
ricecdf,
ricepdf,
riceinv,
ricernd,
ricelike,
ricestat


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



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
ricelike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1530
statistics: nlogL = ricelike ( params , x )
statistics: [ nlogL , acov ] = ricelike ( params , x )
statistics: [&hellip;] = ricelike ( params , x , censor )
statistics: [&hellip;] = ricelike ( params , x , censor , freq )

Negative log-likelihood for the Rician distribution.

nlogL = ricelike ( params , x ) returns the negative
log likelihood of the data in x corresponding to the Rician
distribution with (1) non-centrality (distance) parameter s and (2)
scale parameter sigma given in the two-element vector params .

[ nlogL , acov ] = ricelike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of params are their asymptotic variances.

[&hellip;] = ricelike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = ricelike ( params , x , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

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

See also:
ricecdf,
riceinv,
ricepdf,
ricernd,
ricefit,
ricestat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Negative log-likelihood for the Rician distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
stblfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2563
statistics: paramhat = stblfit ( x )
statistics: [ paramhat , paramci ] = stblfit ( x )
statistics: [ paramhat , paramci ] = stblfit ( x , alpha )
statistics: [ paramhat , paramci ] = stblfit ( x , alpha , freq )
statistics: [ paramhat , paramci ] = stblfit ( x , alpha , options )
statistics: [ paramhat , paramci ] = stblfit ( x , alpha , freq , options )

Estimate parameters and confidence intervals for the stable distribution.

paramhat = stblfit ( x ) returns the maximum likelihood
estimates of the parameters of the stable distribution, in the Nolan
S0 parameterization, given the data in x .
paramhat (1) is the tail index alpha ,
paramhat (2) is the skewness beta , paramhat (3)
is the scale gam , and paramhat (4) is the location
delta .

[ paramhat , paramci ] = stblfit ( x ) returns the 95%
confidence intervals for the parameter estimates. The intervals are Wald
intervals from the observed Fisher information.

[&hellip;] = stblfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default value.

[&hellip;] = stblfit ( x , alpha , freq ) accepts a
frequency vector, freq , of the same size as x . freq
must contain non-negative integer frequencies for the corresponding elements
in x . By default, or if left empty,
freq = ones (size ( x )) .

[ paramhat , paramci ] = stblfit ( x , alpha ,
options ) specifies control parameters for the iterative algorithm used
to compute the ML estimates with the fminsearch function.
options is a structure with the following fields and their default
values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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. Censoring is not supported.

The estimates are the maximum-likelihood estimates under the mathematically
exact density. MATLAB fits an interpolation-based approximation of the stable
density, whose maximum-likelihood estimates deviate from the exact ones by
about 10^{-2} (and the resulting confidence intervals by up to roughly
20%); stblfit returns the exact (more accurate) estimates.

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

See also:
stbllike,
stblpdf,
stblcdf,
stblinv,
stblrnd,
fitdist,
makedist


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



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
stbllike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1314
statistics: nlogL = stbllike ( params , x )
statistics: [ nlogL , acov ] = stbllike ( params , x )
statistics: [ nlogL , acov ] = stbllike ( params , x , freq )

Negative log-likelihood for the stable distribution.

nlogL = stbllike ( params , x ) returns the negative
log-likelihood of the data in x corresponding to the stable
distribution, in the Nolan S0 parameterization, with (1) tail index
alpha , (2) skewness beta , (3) scale gam , and (4) location
delta given in the four-element vector params .

[ nlogL , acov ] = stbllike ( params , x ) also
returns the inverse of the observed Fisher information matrix, acov . If
the input parameter values in params are the maximum likelihood
estimates, the diagonal elements of acov are their asymptotic
variances. acov is based on the numerically evaluated Hessian of the
negative log-likelihood, since the stable density has no closed form.

[&hellip;] = stbllike ( params , x , freq ) accepts a
frequency vector, freq , of the same size as x . freq must
contain non-negative integer frequencies for the corresponding elements in
x . By default, or if left empty, freq = ones (size
( x )) .

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

See also:
stblfit,
stblpdf,
stblcdf,
stblinv,
stblrnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Negative log-likelihood for the stable distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
tlsfit


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2223
statistics: paramhat = tlsfit ( x )
statistics: [ paramhat , paramci ] = tlsfit ( x )
statistics: [ paramhat , paramci ] = tlsfit ( x , alpha )
statistics: [&hellip;] = tlsfit ( x , alpha , censor )
statistics: [&hellip;] = tlsfit ( x , alpha , censor , freq )
statistics: [&hellip;] = tlsfit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for the Location-scale Student&rsquo;s
T distribution.

muhat = tlsfit ( x ) returns the maximum likelihood
estimates of the parameters of the location-scale T distribution
given the data in x . paramhat (1) is the location
parameter, mu , paramhat (2) is the scale parameter,
sigma , and paramhat (3) is the degrees of freedom,
nu .

[ paramhat , paramci ] = tlsfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = tlsfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = tlsfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = tlsfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = tlsfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute ML estimates with the
fminsearch function. options is a structure with the following
fields and their default values:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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:
tlscdf,
tlsinv,
tlspdf,
tlsrnd,
tlslike,
tlsstat


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Estimate parameters and confidence intervals for the Location-scale Student's T distribution.



# name: <cell-element>
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# length: 7
tlslike


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# length: 1727
statistics: nlogL = tlslike ( params , x )
statistics: [ nlogL , acov ] = tlslike ( params , x )
statistics: [&hellip;] = tlslike ( params , x , alpha , censor )
statistics: [&hellip;] = tlslike ( params , x , alpha , censor , freq )

Negative log-likelihood for the location-scale Student&rsquo;s T distribution.

nlogL = tlslike ( params , x ) returns the negative
log-likelihood of the x in x corresponding to the location-scale T
distribution with (1) location parameter mu , (2) scale parameter
sigma and (3) degrees of freedom nu given in the three-element
vector params .

[ nlogL , acov ] = tlslike ( params , x ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances. acov
is based on the observed Fisher&rsquo;s information, not the expected information.

[&hellip;] = tlslike ( params , x , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = tlslike ( params , x , censor ,
freq ) accepts a frequency vector, freq , of the same size as
x . freq typically contains integer frequencies for the
corresponding elements in x , but may contain any non-integer
non-negative values. By default, or if left empty,
freq = ones (size ( x )) .

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:
tlscdf,
tlsinv,
tlspdf,
tlsrnd,
tlsfit,
tlsstat


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Negative log-likelihood for the location-scale Student's T distribution.



# name: <cell-element>
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# elements: 1
# length: 7
unidfit


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statistics: Nhat = unidfit ( x )
statistics: [ Nhat , Nci ] = unidfit ( x )
statistics: [ Nhat , Nci ] = unidfit ( x , alpha )
statistics: [ Nhat , Nci ] = unidfit ( x , alpha , freq )

Estimate parameter and confidence intervals for the discrete uniform
distribution.

Nhat = unidfit ( x ) returns the maximum likelihood estimate
(MLE) of the maximum observable value for the discrete uniform distribution.
x must be a vector.

[ Nhat , Nci ] = unidfit ( x , alpha ) also
returns the 100 * (1 - alpha ) percent confidence intervals of
the estimated parameter. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = unidfit ( x , alpha , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) .

Further information about the discrete uniform distribution can be found at
https://en.wikipedia.org/wiki/Discrete_uniform_distribution

See also:
unidcdf,
unidinv,
unidpdf,
unidrnd,
unidstat


# name: <cell-element>
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Estimate parameter and confidence intervals for the discrete uniform distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
unifit


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statistics: ahat = unifit ( x )
statistics: [ ahat , bhat ] = unifit ( x )
statistics: [ ahat , bhat , aci , bci ] = unifit ( x )
statistics: [&hellip;] = unifit ( x , alpha )
statistics: [&hellip;] = unifit ( x , alpha , freq )

Estimate parameters and confidence intervals for the continuous uniform
distribution.

[ ahat , bhat ] = unifit ( x ) returns the maximum
likelihood estimates of the lower and upper endpoints, a and b ,
of the continuous uniform distribution given the data in x . Each
estimate is returned as a separate output.

x may be a vector, which is fitted as a single sample, or a matrix,
which is fitted column by column. For a matrix of n columns
ahat and bhat are 1 -by- n row vectors and aci
and bci are 2 -by- n .

[ ahat , bhat , aci , bci ] = unifit ( x ) also
returns the 95% confidence intervals of the two estimates, one column per
column of x , with the lower bound in the first row and the upper bound
in the second. ahat is the upper bound of aci and bhat the
lower bound of bci , since no sample can fall outside the fitted range.

[&hellip;] = unifit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals of the
estimated parameters. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = unifit ( x , alpha , freq ) accepts a
frequency vector, freq , of the same size as x . freq
typically contains integer frequencies for the corresponding elements in
x , but it can contain any non-integer non-negative values. By default,
or if left empty, freq = ones (size ( x )) . This third
argument is an Octave extension; MATLAB&rsquo;s unifit takes two inputs at
most, and freq is accepted for a vector x only.

Further information about the continuous uniform distribution can be found at
https://en.wikipedia.org/wiki/Continuous_uniform_distribution

See also:
unifcdf,
unifinv,
unifpdf,
unifrnd,
unifstat


# name: <cell-element>
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Estimate parameters and confidence intervals for the continuous uniform distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
wblfit


# name: <cell-element>
# type: sq_string
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# length: 2192
statistics: paramhat = wblfit ( x )
statistics: [ paramhat , paramci ] = wblfit ( x )
statistics: [ paramhat , paramci ] = wblfit ( x , alpha )
statistics: [&hellip;] = wblfit ( x , alpha , censor )
statistics: [&hellip;] = wblfit ( x , alpha , censor , freq )
statistics: [&hellip;] = wblfit ( x , alpha , censor , freq , options )

Estimate parameters and confidence intervals for the Weibull distribution.

muhat = wblfit ( x ) returns the maximum likelihood
estimates of the parameters of the Weibull distribution given the data in
x . paramhat (1) is the scale parameter, lambda ,
and paramhat (2) is the shape parameter, k .

[ paramhat , paramci ] = wblfit ( x ) returns the 95%
confidence intervals for the parameter estimates.

[&hellip;] = wblfit ( x , alpha ) also returns the
100 * (1 - alpha ) percent confidence intervals for the
parameter estimates. By default, the optional argument alpha is
0.05 corresponding to 95% confidence intervals. Pass in [] for
alpha to use the default values.

[&hellip;] = wblfit ( x , alpha , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = wblfit ( x , alpha , censor , freq )
accepts a frequency vector, freq , of the same size as x .
freq typically contains integer frequencies for the corresponding
elements in x , but it can contain any non-integer non-negative values.
By default, or if left empty, freq = ones (size ( x )) .

[&hellip;] = wblfit (&hellip;, options ) specifies control
parameters for the iterative algorithm used to compute the maximum likelihood
estimates. options is a structure with the following field and its
default value:

options .Display = "off"
options .MaxFunEvals = 400
options .MaxIter = 200
options .TolX = 1e-6

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

The prob.WeibullDistribution class names these same two parameters
A and B , after MATLAB. lambda is its A and
k is its B .

See also:
wblcdf,
wblinv,
wblpdf,
wblrnd,
wbllike,
wblstat


# name: <cell-element>
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Estimate parameters and confidence intervals for the Weibull distribution.



# name: <cell-element>
# type: sq_string
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# length: 7
wbllike


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# length: 1739
statistics: nlogL = wbllike ( params , x )
statistics: [ nlogL , acov ] = wbllike ( params , x )
statistics: [&hellip;] = wbllike ( params , x , alpha , censor )
statistics: [&hellip;] = wbllike ( params , x , alpha , censor , freq )

Negative log-likelihood for the Weibull distribution.

nlogL = wbllike ( params , data ) returns the negative
log-likelihood of the data in x corresponding to the Weibull
distribution with (1) scale parameter lambda and (2) shape parameter
k given in the two-element vector params .

[ nlogL , acov ] = wbllike ( params , data ) also
returns the inverse of Fisher&rsquo;s information matrix, acov . If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances. acov
is based on the observed Fisher&rsquo;s information, not the expected information.

[&hellip;] = wbllike ( params , data , censor ) accepts a
boolean vector, censor , of the same size as x with 1 s for
observations that are right-censored and 0 s for observations that are
observed exactly. By default, or if left empty,
censor = zeros (size ( x )) .

[&hellip;] = wbllike ( params , data , censor ,
freq ) accepts a frequency vector, freq , of the same size as
x . freq typically contains integer frequencies for the
corresponding elements in x , but may contain any non-integer
non-negative values. By default, or if left empty,
freq = ones (size ( x )) .

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

The prob.WeibullDistribution class names these same two parameters
A and B , after MATLAB. lambda is its A and
k is its B .

See also:
wblcdf,
wblinv,
wblpdf,
wblrnd,
wblfit,
wblstat


# name: <cell-element>
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Negative log-likelihood for the Weibull distribution.





