gevcdf
Generalized extreme value cumulative distribution function
Syntax
p = gevcdf(x,k,sigma,mu)
p = gevcdf(x,k,sigma,mu,'upper')
Description
p = gevcdf(x,k,sigma,mu) returns
the cdf of the generalized extreme value (GEV) distribution with shape
parameter k, scale parameter sigma,
and location parameter, mu, evaluated at the values
in 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 k, sigma,
and mu are 0, 1, and 0, respectively.
When 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 w has
a Weibull distribution as computed by the wblcdf
function, then -w has a type III extreme value
distribution and 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 evcdf function.
The mean of the GEV distribution is not finite when k ≥ 1,
and the variance is not finite when k ≥ 1/2.
The GEV distribution has positive density only for values of X such
that k*(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
Version History
Introduced before R2006a
