gevrnd
Generalized extreme value random numbers
Syntax
R = gevrnd(k,sigma,mu)
R = gevrnd(k,sigma,mu,m,n,...)
R = gevrnd(k,sigma,mu,[m,n,...])
Description
R = gevrnd(k,sigma,mu) returns
an array of random numbers chosen from the generalized extreme value
(GEV) distribution with shape parameter k, scale
parameter sigma, and location parameter, mu.
The size of R is the common size of the input arguments
if all are arrays. If any parameter is a scalar, the size of R is
the size of the other parameters.
R = gevrnd(k,sigma,mu,m,n,...) or R = gevrnd(k,sigma,mu,[m,n,...]) generates
an m-by-n-by-... array containing
random numbers from the GEV distribution with parameters k, sigma,
and mu. The k, sigma, mu parameters
can each be scalars or arrays of the same size as R.
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 wblrnd
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 evrnd 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
