Function File: nlogL, Grad, ACOV = gevlike (params, data)

Compute the negative log-likelihood of data under the generalized extreme value (GEV) distribution with given parameter values.

Arguments

• params is the 3-parameter vector [k, sigma, mu], where k is the shape parameter of the GEV distribution, sigma is the scale parameter of the GEV distribution, and mu is the location parameter of the GEV distribution.
• data is the vector of given values.

Return values

• nlogL is the negative log-likelihood.
• Grad is the 3 by 1 gradient vector (first derivative of the negative log likelihood with respect to the parameter values)
• ACOV is the 3 by 3 Fisher information matrix (second derivative of the negative log likelihood with respect to the parameter values)

Examples

x = -5:-1;
k = -0.2;
sigma = 0.3;
mu = 0.5;
[L, ~, C] = gevlike ([k sigma mu], x);

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, gevfit, gevinv, gevpdf, gevrnd, gevstat.

Package: statistics