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gevinv

Generalized extreme value inverse cumulative distribution function

Syntax

X = gevinv(P,k,sigma,mu)

Description

X = gevinv(P,k,sigma,mu) returns the inverse cdf of the generalized extreme value (GEV) distribution with shape parameter k, scale parameter sigma, and location parameter mu, evaluated at the values in P. The size of X is the common size of the input arguments. A scalar input functions as a constant matrix of the same size as the other inputs.

Default values for k, sigma, and mu are 0, 1, and 0, respectively.

When k < 0, the GEV is the type III extreme value distribution. When k > 0, the GEV distribution is the type II, or Frechet, extreme value distribution. If w has a Weibull distribution as computed by the wblinv function, then -w has a type III extreme value distribution and 1/w has a type II extreme value distribution. In the limit as k approaches 0, the GEV is the mirror image of the type I extreme value distribution as computed by the evinv function.

The mean of the GEV distribution is not finite when k1, and the variance is not finite when k1/2. The GEV distribution has positive density only for values of X such that k*(X-mu)/sigma > -1.

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.

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