Syntax

Description

nlogL = gplike(params,data)returns the negative of the loglikelihoodnlogLfor the two-parameter generalized Pareto (GP) distribution, evaluated at parametersparams.params(1)is the tail index (shape) parameter,k, andparams(2)is the scale parameter.gplikedoes not allow a threshold (location) parameter.

[nlogL,acov] = gplike(params,data)returns the inverse of Fisher's information matrix,acov. If the input parameter values inparamsare the maximum likelihood estimates, the diagonal elements ofacovare their asymptotic variances.acovis based on the observed Fisher's information, not the expected information.

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

x > theta, or, when

k < 0, $$0\le \frac{x-\theta }{\sigma }\le -\frac{1}{k}$$.

References

See Also

gpcdf|gpfit|gpinv|gppdf|gprnd|gpstat