Generalized extreme value negative log-likelihood
nlogL = gevlike(params,data)
[nlogL,ACOV] = gevlike(params,data)
nlogL = gevlike(params,data) returns
the negative of the log-likelihood
nlogL for the
generalized extreme value (GEV) distribution, evaluated at parameters
the shape parameter,
the scale parameter,
the location parameter,
[nlogL,ACOV] = gevlike(params,data) returns
the inverse of Fisher's information matrix,
If the input parameter values in
params are the
maximum likelihood estimates, the diagonal elements of
their asymptotic variances.
ACOV is based on the
observed Fisher's information, not the expected information.
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
a Weibull distribution as computed by the
-w has a type III extreme value
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
The mean of the GEV distribution is not finite when
and the variance is not finite when
The GEV distribution has positive density only for values of
k*(X-mu)/sigma > -1.
 Embrechts, P., C. Klüppelberg, and T. Mikosch. Modelling Extremal Events for Insurance and Finance. New York: Springer, 1997.
 Kotz, S., and S. Nadarajah.Extreme Value Distributions: Theory and Applications. London: Imperial College Press, 2000.