gpstat

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) 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/k, the GP is equivalent to a Pareto distribution with a scale parameter equal to sigma/k and a shape parameter equal to 1/k. 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, $$0\le \frac{x-\theta }{\sigma }\le -\frac{1}{k}$$.

References

Extended Capabilities

Version History

Introduced before R2006a

See Also

gppdf | gpcdf | gpinv | gpfit | gplike | gprnd