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gevstat

Generalized extreme value mean and variance

Syntax

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

Description

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

Whenk < 0, the GEV is the type III extreme value distribution. Whenk > 0, the GEV distribution is the type II, or Frechet, extreme value distribution. Ifwhas a Weibull distribution as computed by thewblstatfunction, then-whas a type III extreme value distribution and1/whas a type II extreme value distribution. In the limit askapproaches 0, the GEV is the mirror image of the type I extreme value distribution as computed by theevstatfunction.

The mean of the GEV distribution is not finite whenk1, and the variance is not finite whenk1/2. The GEV distribution has positive density only for values ofXsuch thatk*(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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Introduced before R2006a