Contents

evlike

Extreme value negative log-likelihood

Syntax

nlogL = evlike(params,data)
[nlogL,AVAR] = evlike(params,data)
[...] = evlike(params,data,censoring)
[...] = evlike(params,data,censoring,freq)

Description

nlogL = evlike(params,data) returns the negative of the log-likelihood for the type 1 extreme value distribution. params(1) is the tail location parameter, mu, and params(2) is the scale parameter, sigma. nlogL is a scalar.

[nlogL,AVAR] = evlike(params,data) 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.

[...] = evlike(params,data,censoring) accepts a Boolean vector of the same size as data, which is 1 for observations that are right-censored and 0 for observations that are observed exactly.

[...] = evlike(params,data,censoring,freq) accepts a frequency vector of the same size as data. freq typically contains integer frequencies for the corresponding elements in data, but can contain any nonnegative values. Pass in [] for censoring to use its default value.

The type 1 extreme value distribution is also known as the Gumbel distribution. The version used here is suitable for modeling minima; the mirror image of this distribution can be used to model maxima by negating data. See Extreme Value Distribution for more details. If x has a Weibull distribution, then X = log(x) has the type 1 extreme value distribution.

See Also

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