gevfit
Generalized extreme value parameter estimates
Syntax
parmhat = gevfit(X)
[parmhat,parmci] = gevfit(X)
[parmhat,parmci] = gevfit(X,alpha)
[...] = gevfit(X,alpha,options)
Description
parmhat = gevfit(X) returns
maximum likelihood estimates of the parameters for the generalized
extreme value (GEV) distribution given the data in X. parmhat(1) is
the shape parameter, k, parmhat(2) is
the scale parameter, sigma, and parmhat(3) is
the location parameter, mu.
[parmhat,parmci] = gevfit(X) returns
95% confidence intervals for the parameter estimates.
[parmhat,parmci] = gevfit(X,alpha) returns 100(1-alpha)%
confidence intervals for the parameter estimates.
[...] = gevfit(X,alpha,options) specifies
control parameters for the iterative algorithm used to compute ML
estimates. This argument can be created by a call to statset.
See statset('gevfit') for parameter names and
default values. Pass in [] for alpha to
use the default values.
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 wblfit 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 evfit 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 is defined for 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
