- statistics: [nlogL, Grad, ACOV] = gevlike (params, data)
Compute the negative log-likelihood of data under the generalized extreme
value (GEV) distribution with given parameter values.
Arguments
-
params is the 3-parameter vector [k, sigma, mu],
where k is the shape parameter of the GEV distribution, sigma is
the scale parameter of the GEV distribution, and mu is the location
parameter of the GEV distribution.
-
data is the vector of given values.
Return values
-
nlogL is the negative log-likelihood.
-
Grad is the 3 by 1 gradient vector, which is the first derivative of
the negative log likelihood with respect to the parameter values.
-
ACOV is the 3 by 3 inverse of the Fisher information matrix, which is
the second derivative of the negative log likelihood with respect to the
parameter values.
Examples
| x = -5:-1;
k = -0.2;
sigma = 0.3;
mu = 0.5;
[L, ~, C] = gevlike ([k sigma mu], x);
|
References
-
Rolf-Dieter Reiss and Michael Thomas. Statistical Analysis of Extreme
Values with Applications to Insurance, Finance, Hydrology and Other Fields.
Chapter 1, pages 16-17, Springer, 2007.
See also:
gevcdf,
gevfit,
gevinv,
gevpdf,
gevrnd,
gevstat
Source Code:
gevlike