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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.

     ‘[...] = 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.

     ‘[...] = 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'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.

     ‘[...] = 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: [...] = 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'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.

     ‘[...] = 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: [...] = bisafit (X, ALPHA, CENSOR)
 -- statistics: [...] = bisafit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = bisafit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = bisafit (..., 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: [...] = bisalike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = bisalike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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: [...] = burrfit (X, ALPHA, CENSOR)
 -- statistics: [...] = burrfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = burrfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = burrfit (..., 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: [...] = burrlike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = burrlike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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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evfit


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 -- statistics: PARAMHAT = evfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = evfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = evfit (X, ALPHA)
 -- statistics: [...] = evfit (X, ALPHA, CENSOR)
 -- statistics: [...] = evfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = evfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = evfit (..., 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
distributi...



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evlike


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 -- statistics: NLOGL = evlike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = evlike (PARAMS, X)
 -- statistics: [...] = evlike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = evlike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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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expfit


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 -- statistics: MUHAT = expfit (X)
 -- statistics: [MUHAT, MUCI] = expfit (X)
 -- statistics: [MUHAT, MUCI] = expfit (X, ALPHA)
 -- statistics: [...] = expfit (X, ALPHA, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = 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.

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

     ‘[...] = 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's ‘expfit’ produces unpredictable
     results for some cases with higher dimensions (specifically 1 x m x
     n x ...  arrays).  Octave's implementation allows for nxD 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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Estimate mean and confidence intervals for the exponential distribution.



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explike


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 -- statistics: NLOGL = explike (MU, X)
 -- statistics: [NLOGL, AVAR] = explike (MU, X)
 -- statistics: [...] = explike (MU, X, CENSOR)
 -- statistics: [...] = 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's information matrix, AVAR.  If the input mean parameter,
     MU, is the maximum likelihood estimate, AVAR is its asymptotic
     variance.

     ‘[...] = explike (MU, X, CENSOR)’ accepts a boolean vector, CENSOR,
     of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the exponential distribution.



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gamfit


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 -- statistics: PARAMHAT = gamfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = gamfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = gamfit (X, ALPHA)
 -- statistics: [...] = gamfit (X, ALPHA, CENSOR)
 -- statistics: [...] = gamfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = gamfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = gamfit (..., 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.


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Estimate parameters and confidence intervals for the Gamma distribution.



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gamlike


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 -- statistics: NLOGL = gamlike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = gamlike (PARAMS, X)
 -- statistics: [...] = gamlike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = gamlike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the Gamma distribution.



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geofit


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 -- 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.

     ‘[...] = 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.


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Estimate parameter and confidence intervals for the geometric
distribution.



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gevfit


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 -- 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.

     ‘[...] = 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.

     ‘[...] = 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.


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Estimate parameters and confidence intervals for the generalized extreme
valu...



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gevfit_lmom


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 -- 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)

     See also: gevfit.

     References
     ----------

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


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Find an estimator (PARAMHAT) of the generalized extreme value (GEV)
distribut...



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gevlike


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 -- 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'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.

     ‘[...] = 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.

     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.


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



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gpfit


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 -- statistics: PARAMHAT = gpfit (X, THETA)
 -- statistics: [PARAMHAT, PARAMCI] = gpfit (X, THETA)
 -- statistics: [PARAMHAT, PARAMCI] = gpfit (X, THETA, ALPHA)
 -- statistics: [PARAMHAT, PARAMCI] = gpfit (X, THETA, ALPHA, OPTIONS)

     Estimate parameters and confidence intervals for the generalized
     Pareto distribution.

     ‘PARAMHAT = gpfit (X, THETA)’ returns the maximum likelihood
     estimates of the parameters of the generalized Pareto distribution
     given the data in X and the location parameter THETA.  PARAMHAT(1)
     is the shape parameter, K, PARAMHAT(2) is the scale parameter,
     SIGMA, and PARAMHAT(3) is the location parameter, THETA.  Although
     THETA is returned in the estimated PARAMHAT, ‘gpfit’ does not
     estimate the location parameter THETA, and it must be assumed to be
     known, given as a fixed parameter in input argument THETA.

     ‘[PARAMHAT, PARAMCI] = gpfit (X, THETA)’ returns the 95% confidence
     intervals for the estimated parameter K and SIGMA.  The third
     column of PARAMCI includes the location parameter THETA without any
     confidence bounds.

     ‘[...] = gpfit (X, THETA, 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.

     ‘[...] = gpfit (X, THETA, 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 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.


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Estimate parameters and confidence intervals for the generalized Pareto
distr...



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gplike


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 -- statistics: NLOGL = gplike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = gplike (PARAMS, X)
 -- statistics: [...] = 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, (2) scale parameter SIGMA, and (3)
     location parameter THETA given in the three-element vector PARAMS.

     ‘[NLOGL, ACOV] = gplike (PARAMS, X)’ returns the inverse of
     Fisher'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's information, not the expected information.

     ‘[...] = 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)).

     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.


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Negative log-likelihood for the generalized Pareto distribution.



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gumbelfit


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 -- statistics: PARAMHAT = gumbelfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = gumbelfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = gumbelfit (X, ALPHA)
 -- statistics: [...] = gumbelfit (X, ALPHA, CENSOR)
 -- statistics: [...] = gumbelfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = gumbelfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = gumbelfit (..., 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.


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Estimate parameters and confidence intervals for Gumbel distribution.



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gumbellike


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 -- statistics: NLOGL = gumbellike (PARAMS, X)
 -- statistics: [NLOGL, AVAR] = gumbellike (PARAMS, X)
 -- statistics: [...] = gumbellike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = gumbellike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the extreme value distribution.



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hnfit


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 -- 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.

     ‘[...] = 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.

     ‘[...] = 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.


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



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hnlike


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 -- 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'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.

     ‘[...] = 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.


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Negative log-likelihood for the half-normal distribution.



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invgfit


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 -- statistics: PARAMHAT = invgfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = invgfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = invgfit (X, ALPHA)
 -- statistics: [...] = invgfit (X, ALPHA, CENSOR)
 -- statistics: [...] = invgfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = invgfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = invgfit (..., 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.


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Estimate mean and confidence intervals for the inverse Gaussian
distribution.



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invglike


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 -- statistics: NLOGL = invglike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = invglike (PARAMS, X)
 -- statistics: [...] = invglike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = invglike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the inverse Gaussian distribution.



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logifit


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 -- statistics: PARAMHAT = logifit (X)
 -- statistics: [PARAMHAT, PARAMCI] = logifit (X)
 -- statistics: [PARAMHAT, PARAMCI] = logifit (X, ALPHA)
 -- statistics: [...] = logifit (X, ALPHA, CENSOR)
 -- statistics: [...] = logifit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = logifit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = logifit (..., 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.


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Estimate mean and confidence intervals for the logistic distribution.



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logilike


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 -- statistics: NLOGL = logilike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = logilike (PARAMS, X)
 -- statistics: [...] = logilike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = logilike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the logistic distribution.



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loglfit


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 -- statistics: PARAMHAT = loglfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = loglfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = loglfit (X, ALPHA)
 -- statistics: [...] = loglfit (X, ALPHA, CENSOR)
 -- statistics: [...] = loglfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = loglfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = loglfit (..., 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.


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



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logllike


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 -- statistics: NLOGL = logllike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = logllike (PARAMS, X)
 -- statistics: [...] = logllike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = logllike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the log-logistic distribution.



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lognfit


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 -- statistics: PARAMHAT = lognfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = lognfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = lognfit (X, ALPHA)
 -- statistics: [...] = lognfit (X, ALPHA, CENSOR)
 -- statistics: [...] = lognfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = lognfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = lognfit (..., 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.


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Estimate parameters and confidence intervals for the lognormal
distribution.



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lognlike


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 -- statistics: NLOGL = lognlike (PARAMS, X)
 -- statistics: [NLOGL, AVAR] = lognlike (PARAMS, X)
 -- statistics: [...] = lognlike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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's information, not the expected information.

     ‘[...] = lognlike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the lognormal distribution.



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nakafit


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 -- statistics: PARAMHAT = nakafit (X)
 -- statistics: [PARAMHAT, PARAMCI] = nakafit (X)
 -- statistics: [PARAMHAT, PARAMCI] = nakafit (X, ALPHA)
 -- statistics: [...] = nakafit (X, ALPHA, CENSOR)
 -- statistics: [...] = nakafit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = nakafit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = nakafit (..., 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.


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Estimate mean and confidence intervals for the Nakagami distribution.



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nakalike


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 -- statistics: NLOGL = nakalike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = nakalike (PARAMS, X)
 -- statistics: [...] = nakalike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = nakalike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the Nakagami distribution.



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nbinfit


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 -- 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.

     ‘[...] = 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
distrib...



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nbinlike


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 -- 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'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.

     ‘[...] = 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.


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Negative log-likelihood for the negative binomial distribution.



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normfit


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 -- statistics: MUHAT = normfit (X)
 -- statistics: [MUHAT, SIGMAHAT] = normfit (X)
 -- statistics: [MUHAT, SIGMAHAT, MUCI] = normfit (X)
 -- statistics: [MUHAT, SIGMAHAT, MUCI, SIGMACI] = normfit (X)
 -- statistics: [...] = normfit (X, ALPHA)
 -- statistics: [...] = normfit (X, ALPHA, CENSOR)
 -- statistics: [...] = normfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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
          100x(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 ‘(SUM (FREQ) - 1) / SUM (FREQ)’.  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.


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Estimate parameters and confidence intervals for the normal
distribution.



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normlike


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 -- statistics: NLOGL = normlike (PARAMS, X)
 -- statistics: [NLOGL, AVAR] = normlike (PARAMS, X)
 -- statistics: [...] = normlike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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's information, not the expected information.

     ‘[...] = 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.

     ‘[...] = 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.


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Negative log-likelihood for the normal distribution.



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poissfit


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 -- 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.

     ‘[...] = 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.


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Estimate parameter and confidence intervals for the Poisson
distribution.



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poisslike


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 -- statistics: NLOGL = poisslike (LAMBDA, X)
 -- statistics: [NLOGL, AVAR] = poisslike (LAMBDA, X)
 -- statistics: [...] = 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's information matrix, AVAR.  If the input rate parameter,
     LAMBDA, is the maximum likelihood estimate, AVAR is its asymptotic
     variance.

     ‘[...] = 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.


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Negative log-likelihood for the Poisson distribution.



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raylfit


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 -- 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.

     ‘[...] = raylfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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>

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


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Estimate parameter and confidence intervals for the Rayleigh
distribution.



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rayllike


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 -- statistics: NLOGL = rayllike (SIGMA, X)
 -- statistics: [NLOGL, ACOV] = rayllike (SIGMA, X)
 -- statistics: [...] = 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's information matrix, ACOV.  If the input rate parameter,
     SIGMA, is the maximum likelihood estimate, ACOV is its asymptotic
     variance.

     ‘[...] = 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>

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


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Negative log-likelihood for the Rayleigh distribution.



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ricefit


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 -- statistics: PARAMHAT = ricefit (X)
 -- statistics: [PARAMHAT, PARAMCI] = ricefit (X)
 -- statistics: [PARAMHAT, PARAMCI] = ricefit (X, ALPHA)
 -- statistics: [...] = ricefit (X, ALPHA, CENSOR)
 -- statistics: [...] = ricefit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = ricefit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = ricefit (..., 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.


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Estimate parameters and confidence intervals for the Rician
distribution.



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ricelike


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 -- statistics: NLOGL = ricelike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = ricelike (PARAMS, X)
 -- statistics: [...] = ricelike (PARAMS, X, CENSOR)
 -- statistics: [...] = 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'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.

     ‘[...] = ricelike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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.


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Negative log-likelihood for the Rician distribution.



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tlsfit


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 -- statistics: PARAMHAT = tlsfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = tlsfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = tlsfit (X, ALPHA)
 -- statistics: [...] = tlsfit (X, ALPHA, CENSOR)
 -- statistics: [...] = tlsfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = tlsfit (X, ALPHA, CENSOR, FREQ, OPTIONS)

     Estimate parameters and confidence intervals for the Location-scale
     Student'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.

     ‘[...] = 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.

     ‘[...] = tlsfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = tlsfit (..., 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.TolX = 1e-6

     Further information about the location-scale Student'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...



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tlslike


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 -- statistics: NLOGL = tlslike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = tlslike (PARAMS, X)
 -- statistics: [...] = tlslike (PARAMS, X, ALPHA, CENSOR)
 -- statistics: [...] = tlslike (PARAMS, X, ALPHA, CENSOR, FREQ)

     Negative log-likelihood for the location-scale Student'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'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's information, not the expected information.

     ‘[...] = tlslike (PARAMS, X, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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'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.



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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.

     ‘[...] = 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.


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Estimate parameter and confidence intervals for the discrete uniform
distribu...



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unifit


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 -- statistics: PARAMHAT = unifit (X)
 -- statistics: [PARAMHAT, PARAMCI] = unifit (X)
 -- statistics: [PARAMHAT, PARAMCI] = unifit (X, ALPHA)
 -- statistics: [PARAMHAT, PARAMCI] = unifit (X, ALPHA, FREQ)

     Estimate parameter and confidence intervals for the continuous
     uniform distribution.

     ‘PARAMHAT = unifit (X)’ returns the maximum likelihood estimate
     (MLE) of the parameters A and B of the continuous uniform
     distribution given the data in X.  X must be a vector.

     ‘[PARAMHAT, PARAMCI] = unifit (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.

     ‘[...] = 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)).

     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.


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Estimate parameter and confidence intervals for the continuous uniform
distri...



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wblfit


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 -- statistics: PARAMHAT = wblfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = wblfit (X)
 -- statistics: [PARAMHAT, PARAMCI] = wblfit (X, ALPHA)
 -- statistics: [...] = wblfit (X, ALPHA, CENSOR)
 -- statistics: [...] = wblfit (X, ALPHA, CENSOR, FREQ)
 -- statistics: [...] = 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.

     ‘[...] = 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.

     ‘[...] = wblfit (X, ALPHA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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)).

     ‘[...] = wblfit (..., 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>

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


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Estimate parameters and confidence intervals for the Weibull
distribution.



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wbllike


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 -- statistics: NLOGL = wbllike (PARAMS, X)
 -- statistics: [NLOGL, ACOV] = wbllike (PARAMS, X)
 -- statistics: [...] = wbllike (PARAMS, X, ALPHA, CENSOR)
 -- statistics: [...] = 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'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's information, not the expected information.

     ‘[...] = wbllike (PARAMS, DATA, CENSOR)’ accepts a boolean vector,
     CENSOR, of the same size as X with 1s for observations that are
     right-censored and 0s for observations that are observed exactly.
     By default, or if left empty, CENSOR = zeros (size (X)).

     ‘[...] = 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>

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


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Negative log-likelihood for the Weibull distribution.





