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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) parameterk, scale parametersigma, and threshold (location) parameter,theta. The size ofris the common size of the input arguments if all are arrays. If any parameter is a scalar, the size ofris the size of the other parameters.

r = gprnd(k,sigma,theta,m,n,...)orR = gprnd(K,sigma,theta,[m,n,...])generates anm-by-n-by-... array. Thek,sigma,thetaparameters can each be scalars or arrays of the same size asr.

Whenk = 0andtheta = 0, the GP is equivalent to the exponential distribution. Whenk > 0andtheta = sigma/k, the GP is equivalent to a Pareto distribution with a scale parameter equal tosigma/kand a shape parameter equal to1/k. The mean of the GP is not finite whenk≥1, and the variance is not finite whenk≥1/2. Whenk≥0, the GP has positive density for

x > theta, or, when

0 ≤ x − θ σ ≤ − 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

See Also

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Topics

Introduced before R2006a

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