Generalized extreme value mean and variance


[M,V] = gevstat(k,sigma,mu)


[M,V] = gevstat(k,sigma,mu) returns the mean of and variance for the generalized extreme value (GEV) distribution with shape parameter k, scale parameter sigma, and location parameter, mu. The sizes of M and V are the common size of the input arguments. A scalar input functions as a constant matrix of the same size as the other inputs.

Default values for k, sigma, and mu are 0, 1, and 0, respectively.

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 wblstat 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 evstat 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.

Introduced before R2006a

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