gpfit
Generalized Pareto parameter estimates
Syntax
parmhat = gpfit(x)
[parmhat,parmci] = gpfit(x)
[parmhat,parmci] = gpfit(x,alpha)
[...] = gpfit(x,alpha,options)
Description
parmhat = gpfit(x) returns
maximum likelihood estimates of the parameters for the two-parameter
generalized Pareto (GP) distribution given the data in x.
parmhat(1) is the tail index (shape) parameter, k and parmhat(2) is
the scale parameter, sigma. gpfit does
not fit a threshold (location) parameter.
[parmhat,parmci] = gpfit(x) returns
95% confidence intervals for the parameter estimates.
[parmhat,parmci] = gpfit(x,alpha) returns 100(1-alpha)%
confidence intervals for the parameter estimates.
[...] = gpfit(x,alpha,options) specifies
control parameters for the iterative algorithm used to compute ML
estimates. This argument can be created by a call to statset.
See statset('gpfit') for parameter names and
default values.
Other functions for the generalized Pareto, such as gpcdf allow
a threshold parameter, theta. However, gpfit does
not estimate theta. It is assumed to be known, and subtracted from x before
calling gpfit.
When k = 0 and theta = 0,
the GP is equivalent to the exponential distribution. When k
> 0 and theta = sigma/k, the GP is
equivalent to a Pareto distribution with a scale parameter equal to sigma/k and
a shape parameter equal to 1/k. The mean of the
GP is not finite when k ≥ 1,
and the variance is not finite when k ≥ 1/2.
When k ≥ 0, the GP has
positive density for
k > theta, or, when k < 0,
for
References
[1] Embrechts, P., C. Klüppelberg, and T. Mikosch. Modelling Extremal Events for Insurance and Finance. New York: Springer, 1997.
[2] Kotz, S., and S. Nadarajah. Extreme Value Distributions: Theory and Applications. London: Imperial College Press, 2000.
Extended Capabilities
Version History
Introduced before R2006a
