gevpdf
Generalized extreme value probability density function
Syntax
Y = gevpdf(X,k,sigma,mu)
Description
Y = gevpdf(X,k,sigma,mu) returns
the pdf 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 Y is 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 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 wblpdf
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
