gpfit
Parameter estimates and confidence intervals for generalized Pareto data.
paramhat = gpfit (x)
returns maximum likelihood estimates
of the parameters of the two-parameter generalized Pareto distribution given
the data in x. params(1) is the SHAPE parameter and
params(2) is the SCALE parameter. gpfit
does not fit a LOCATION
parameter.
[paramhat, paramci] = gpfit (x)
returns 95%
confidence intervals for the parameter estimates.
[…] = gpfit (x, alpha)
returns 100*(1 - alpha)
percent confidence intervals for the parameter estimates.
Pass in [] for alpha to use the default values.
[…] = gpfit (x, alpha, options)
specifies
control parameters for the iterative algorithm used to compute ML estimates
with the fminsearch
function. options is a structure with the
following fields {default values}:
Other functions for the generalized Pareto, such as gpcdf
, allow a
LOCATION parameter. However, gpfit
does not estimate LOCATION, and it
must be assumed known, and subtracted from x before calling
gpfit
.
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, gplike, gpstat
Source Code: gpfit