gpcdf

Generalized Pareto cumulative distribution function

Syntax

p = gpcdf(x,k,sigma,theta)
p = gpcdf(x,k,sigma,theta,'upper')


Description

p = gpcdf(x,k,sigma,theta) returns the cdf 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.

p = gpcdf(x,k,sigma,theta,'upper') returns the complement of the cdf of the generalized Pareto (GP) distribution, using an algorithm that more accurately computes the extreme upper tail probabilities.

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/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

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

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™.

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