Syntax

Description

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

p = gpcdf(x,k,sigma,theta,'upper')returns the complement of the cdf of the generalized Pareto (GP) distribution, using an algorithm that more accurately computes the extreme upper tail probabilities.

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

cdf|gppdf|gpinv|gpstat|gpfit|gplike|gprnd