gplike
Negative log-likelihood for the generalized Pareto distribution.
nlogL = gplike (params, data)
returns the negative
of the log-likelihood for the two-parameter generalized Pareto distribution,
evaluated at params(1) = SHAPE
and
params(2) = SCALE
given data. gplike
does not
allow a LOCATION parameter. nlogL is a scalar.
[nlogL, avar] = gplike (params, data)
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 shape = 0 and location = 0, the generalized Pareto
distribution is equivalent to the exponential distribution. When
shape > 0
and location = scale / shape
,
the generalized Pareto distribution is equivalent to the Pareto distribution.
The mean of the generalized Pareto distribution is not finite when
shape >= 1
, and the variance is not finite when
shape >= 1/2
. When shape >= 0
, the generalized
Pareto distribution has positive density for x > location
,
or, when shape < 0
, for
0 <= (x - location) / scale <= -1 / shape
.
See also: gpcdf, gpinv, gppdf, gprnd, gpfit, gpstat
Source Code: gplike