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 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

$$0\le \frac{x-\theta }{\sigma }\le -\frac{1}{k}$$

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The generated code can return a different sequence of numbers than MATLAB^® if either of the following is true:

• The output is nonscalar.

• An input parameter is invalid for the distribution.

For more information on code generation, see Introduction to Code Generation and General Code Generation Workflow.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a