gpstatGeneralized Pareto mean and variance
Syntax
[M,V] = gpstat(X,K,sigma,theta)Description[M,V] = gpstat(X,K,sigma,theta) returns
the mean of and variance for the generalized Pareto (GP) distribution with
the tail index (shape) parameter K, scale parameter sigma,
and threshold (location) parameter, theta.The default value for theta is 0.When K = 0 and theta = 0, the
GP is equivalent to the exponential distribution. When K > 0 and theta
= sigma, the GP is equivalent to the Pareto distribution. The mean
of the GP is not finite when K ≥ 1,
and the variance is not finite when K ≥ 1/2.
When K ≥ 0, the GP has positive
density for X > theta, or when K < 0,
.References