Syntax

Description

parmhat = gpfit(x)returns maximum likelihood estimates of the parameters for the two-parameter generalized Pareto (GP) distribution given the data inx.parmhat(1)is the tail index (shape) parameter,kandparmhat(2)is the scale parameter,sigma.gpfitdoes not fit a threshold (location) parameter.

[parmhat,parmci] = gpfit(x)returns 95% confidence intervals for the parameter estimates.

[parmhat,parmci] = gpfit(x,alpha)returns100(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 tostatset. Seestatset('gpfit')for parameter names and default values.

Other functions for the generalized Pareto, such asgpcdfallow a threshold parameter,theta. However,gpfitdoes not estimate theta. It is assumed to be known, and subtracted fromxbefore callinggpfit.

Whenk = 0andtheta = 0, the GP is equivalent to the exponential distribution. Whenk > 0andtheta = sigma/k, the GP is equivalent to a Pareto distribution with a scale parameter equal tosigma/kand a shape parameter equal to1/k. The mean of the GP is not finite whenk≥1, and the variance is not finite whenk≥1/2. Whenk≥0, the GP has positive density for

k > theta, or, whenk<0, for

References

See Also

gpcdf|gpinv|gplike|gppdf|gprnd|gpstat|mle