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gevrnd - Generalized extreme value random numbers

Syntax

R = gevrnd(K,sigma,mu)
R = gevrnd(K,sigma,mu,M,N,...)
R = gevrnd(K,sigma,mu,[M,N,...])

Description

R = gevrnd(K,sigma,mu) returns an array of random numbers chosen from the generalized extreme value (GEV) distribution with shape parameter K, scale parameter sigma, and location parameter, mu. The size of R is the common size of the input arguments if all are arrays. If any parameter is a scalar, the size of R is the size of the other parameters.

R = gevrnd(K,sigma,mu,M,N,...) or

R = gevrnd(K,sigma,mu,[M,N,...]) returns an m-by-n-by-... array.

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 wblrnd 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 evrnd 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.

References

[1] Embrechts, P., C. Klüppelberg, and T. Mikosch. Modelling Extremal Events for Insurance and Finance. New York: Springer, 1997.

[2] Kotz, S., and S. Nadarajah. Extreme Value Distributions: Theory and Applications. London: Imperial College Press, 2000.

See Also

random, gevpdf, gevcdf, gevinv, gevstat, gevfit, gevlike

Generalized Extreme Value Distribution

gevpdf

gevstat

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