Generalized Pareto inverse cumulative distribution function


x = gpinv(p,k,sigma,theta)


x = gpinv(p,k,sigma,theta) returns the inverse cdf for a generalized Pareto (GP) distribution with tail index (shape) parameter k, scale parameter sigma, and threshold (location) parameter theta, 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 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 k1, and the variance is not finite when k1/2. When k0, the GP has positive density for

x > theta, or, when

k < 0, 0xθσ1k.


[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

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