gplike
Negative log-likelihood for the generalized Pareto distribution.
nlogL = gplike (params, x)
returns the negative
log-likelihood of the data in x corresponding to the generalized Pareto
distribution with (1) shape parameter k and (2) scale parameter
sigma given in the two-element vector params. gplike
does not allow a location parameter and it must be assumed known, and
subtracted from x before calling gplike
.
[nlogL, acov] = gplike (params, x)
returns
the inverse of Fisher’s information matrix, acov. If the input
parameter values in params are the maximum likelihood estimates, the
diagonal elements of acov are their asymptotic variances. acov
is based on the observed Fisher’s information, not the expected information.
When k = 0
and mu = 0
, the Generalized Pareto CDF
is equivalent to the exponential distribution. When k > 0
and
mu = k / k
the Generalized Pareto is equivalent to
the Pareto distribution. The mean of the Generalized Pareto is not finite
when k >= 1
and the variance is not finite when
k >= 1/2
. When k >= 0
, the Generalized Pareto
has positive density for x > mu
, or, when
mu < 0
, for
0 <= (x - mu) / sigma <= -1 / k
.
Further information about the generalized Pareto distribution can be found at https://en.wikipedia.org/wiki/Generalized_Pareto_distribution
See also: gpcdf, gpinv, gppdf, gprnd, gpfit, gpstat
Source Code: gplike