Statistics: gevlike

### Function Reference: `gevlike`

statistics: nlogL = gevlike (params, x)
statistics: [nlogL, acov] = gevlike (params, x)

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.

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

### References

1. Rolf-Dieter Reiss and Michael Thomas. Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields. Chapter 1, pages 16-17, Springer, 2007.

See also: gevcdf, gevinv, gevpdf, gevrnd, gevfit, gevstat

Source Code: gevlike