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Generalized extreme value random numbers


R = gevrnd(k,sigma,mu)
R = gevrnd(k,sigma,mu,m,n,...)
R = gevrnd(k,sigma,mu,[m,n,...])


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,...]) generates an m-by-n-by-... array containing random numbers from the GEV distribution with parameters k, sigma, and mu. The k, sigma, mu parameters can each be scalars or arrays of the same size as R.

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 k1, and the variance is not finite when k1/2. The GEV distribution has positive density only for values of X such that k*(X-mu)/sigma > -1.


[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.

Extended Capabilities

Version History

Introduced before R2006a