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 ofM
andV
are 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. Ifw
has a Weibull distribution as computed by thewblstat
function, then-w
has a type III extreme value distribution and1/w
has a type II extreme value distribution. In the limit ask
approaches 0, the GEV is the mirror image of the type I extreme value distribution as computed by theevstat
function.
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 ofX
such 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.