Syntax

Description

[m,v] = gpstat(k,sigma,theta)returns the mean of and variance for the generalized Pareto (GP) distribution with the tail index (shape) parameterk, scale parametersigma, and threshold (location) parameter,theta.

The default value forthetais 0.

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 forx > theta, or when

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

References

Extended Capabilities

See Also

gpcdf|gpfit|gpinv|gplike|gppdf|gprnd