### Function Reference: `gevlike`

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

Source Code: gevlike