Contents

evfit

Extreme value parameter estimates

Syntax

parmhat = evfit(data)
[parmhat,parmci] = evfit(data)
[parmhat,parmci] = evfit(data,alpha)
[...] = evfit(data,alpha,censoring)
[...] = evfit(data,alpha,censoring,freq)
[...] = evfit(data,alpha,censoring,freq,options)

Description

parmhat = evfit(data) returns maximum likelihood estimates of the parameters of the type 1 extreme value distribution given the data in the vector data. parmhat(1) is the location parameter, µ, and parmhat(2) is the scale parameter, σ.

[parmhat,parmci] = evfit(data) returns 95% confidence intervals for the parameter estimates on the µ and σ parameters in the 2-by-2 matrix parmci. The first column of the matrix of the extreme value fit contains the lower and upper confidence bounds for the parameter µ, and the second column contains the confidence bounds for the parameter σ.

[parmhat,parmci] = evfit(data,alpha) returns 100(1 - alpha)% confidence intervals for the parameter estimates, where alpha is a value in the range [0 1] specifying the width of the confidence intervals. By default, alpha is 0.05, which corresponds to 95% confidence intervals.

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

[...] = evfit(data,alpha,censoring,freq) accepts a frequency vector, freq of the same size as data. Typically, freq contains integer frequencies for the corresponding elements in data, but can contain any nonnegative values. Pass in [] for alpha, censoring, or freq to use their default values.

[...] = evfit(data,alpha,censoring,freq,options) accepts a structure, options, that specifies control parameters for the iterative algorithm the function uses to compute maximum likelihood estimates. You can create options using the function statset. Enter statset('evfit') to see the names and default values of the parameters that evfit accepts in the options structure. See the reference page for statset for more information about these options.

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 X. 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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