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# gpinv

Generalized Pareto inverse cumulative distribution function

## Syntax

X = gpinv(P,K,sigma,theta)

## Description

X = gpinv(P,K,sigma,theta) returns the inverse cdf for a generalized Pareto (GP) distribution with tail index (shape) parameter K, scale parameter sigma, and threshold (location) parameter theta, evaluated at the values in P. The size of X is 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 for K, sigma, and theta are 0, 1, and 0, respectively.

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 the Pareto distribution. The mean of the GP is not finite when K1, and the variance is not finite when K1/2. When K0, the GP has positive density for

X > theta, or, when

K < 0, $0\le \text{\hspace{0.17em}}\frac{x-\theta }{\sigma }\text{\hspace{0.17em}}\le \text{\hspace{0.17em}}-\frac{1}{k}$.