Statistics Toolbox™

gppdf - Generalized Pareto probability density function

Syntax

P = gppdf(X,K,sigma,theta)

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, 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

pdf, gpcdf, gpinv, gpstat, gpfit, gplike, gprnd

gplike

gplotmatrix