Syntax

Description

x = gpinv(p,k,sigma,theta)returns the inverse cdf for a generalized Pareto (GP) distribution with tail index (shape) parameterk, scale parametersigma, and threshold (location) parametertheta, evaluated at the values inp. The size ofxis the common size of the input arguments. A scalar input functions as a constant matrix of the same size as the other inputs.

Default values fork,sigma, andthetaare 0, 1, and 0, respectively.

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

Extended Capabilities

See Also

gpcdf|gpfit|gplike|gppdf|gprnd|gpstat|icdf