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
and location parameter,
mu. The sizes of
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
mu are 0, 1, and 0, respectively.
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
a Weibull distribution as computed by the
-w has a type III extreme value
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
The mean of the GEV distribution is not finite when
and the variance is not finite when
The GEV distribution has positive density only for values of
k*(X-mu)/sigma > -1.
 Embrechts, P., C. Klüppelberg, and T. Mikosch. Modelling Extremal Events for Insurance and Finance. New York: Springer, 1997.
 Kotz, S., and S. Nadarajah. Extreme Value Distributions: Theory and Applications. London: Imperial College Press, 2000.