Statistics Toolbox™

gprnd - Generalized Pareto random numbers

Syntax

R = gprnd(K,sigma,theta)
R = gprnd(K,sigma,theta,M,N,...)
R = gprnd(K,sigma,theta,[M,N,...])

Description

R = gprnd(K,sigma,theta) returns an array of random numbers chosen from the generalized Pareto (GP) distribution with tail index (shape) parameter K, scale parameter sigma, and threshold (location) parameter, theta. The size of R is the common size of the input arguments if all are arrays. If any parameter is a scalar, the size of R is the size of the other parameters.

Default values for K, sigma, and theta are 0, 1, and 0, respectively.

R = gprnd(K,sigma,theta,M,N,...) or R = gprnd(K,sigma,theta,[M,N,...]) returns an m-by-n-by-... array.

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

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

random, gppdf, gpcdf, gpinv, gpstat, gpfit, gplike

gplotmatrix

gpstat