Statistics Toolbox™

gpstat - Generalized 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

[1] Embrechts, P., C. Klüppelberg, and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance, Springer.

[2] Kotz, S. and S. Nadarajah (2001) Extreme Value Distributions: Theory and Applications, World Scientific Publishing Company.

See Also

gppdf, gpcdf, gpinv, gpfit, gplike, gprnd

gprnd

grp2idx