gppdf

Syntax

Description

p = gppdf(x,k,sigma,theta) returns the pdf of the generalized Pareto (GP) distribution with the tail index (shape) parameter k, scale parameter sigma, and threshold (location) parameter, theta, evaluated at the values in x. The size of p 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 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

pdf | gpcdf | gpinv | gpstat | gpfit | gplike | gprnd