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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.





