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# 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 sample data in `data`. The sample data `data` must be a double-precision vector. `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

### Topics

Introduced before R2006a

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