Syntax

Description

Y = gevpdf(X,k,sigma,mu)returns the pdf of the generalized extreme value (GEV) distribution with shape parameterk, scale parametersigma, and location parameter,mu, evaluated at the values inX. The size ofYis 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 fork,sigma, andmuare 0, 1, and 0, respectively.

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 thewblpdffunction, 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 theevcdffunction.

The mean of the GEV distribution is not finite whenk≥1, and the variance is not finite whenk≥1/2. The GEV distribution has positive density only for values ofXsuch thatk*(X-mu)/sigma > -1.

References

Extended Capabilities

See Also

pdf|gevcdf|gevinv|gevstat|gevfit|gevlike|gevrnd