Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

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.

r = gprnd(k,sigma,theta,m,n,...) or R = gprnd(K,sigma,theta,[m,n,...]) generates an m-by-n-by-... array. The k, sigma, theta parameters can each be scalars or arrays of the same size as r.

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 k1, and the variance is not finite when k1/2. When k0, the GP has positive density for

x > theta, or, when

0xθσ1k

References

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

[2] Kotz, S., and S. Nadarajah. Extreme Value Distributions: Theory and Applications. London: Imperial College Press, 2000.

See Also

| | | | | |

Introduced before R2006a

Was this topic helpful?