Main Content


Generalized extreme value parameter estimates


parmhat = gevfit(X)
[parmhat,parmci] = gevfit(X)
[parmhat,parmci] = gevfit(X,alpha)
[...] = gevfit(X,alpha,options)


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 k1, and the variance is not finite when k1/2. The GEV distribution is defined for k*(X-mu)/sigma > -1.


[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