Function Reference: gevlike

statistics: [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, which is the first derivative of the negative log likelihood with respect to the parameter values.
  • ACOV is the 3 by 3 inverse of the Fisher information matrix, which is the 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

Source Code: gevlike