Generalized extreme value cumulative distribution function
p = gevcdf(x,k,sigma,mu)
p = gevcdf(x,k,sigma,mu,'upper')
p = gevcdf(x,k,sigma,mu) returns
the cdf of the generalized extreme value (GEV) distribution with shape
k, scale parameter
and location parameter,
mu, evaluated at the values
x. The size of
p is the
common size of the input arguments. A scalar input functions as a
constant matrix of the same size as the other inputs.
p = gevcdf(x,k,sigma,mu,'upper') returns
the complement of the cdf of the GEV distribution, using an algorithm
that more accurately computes the extreme upper tail probabilities.
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.