gpstat - Generalized Pareto mean and variance
Syntax
[M,V] = gpstat(K,sigma,theta)
Description
[M,V] = gpstat(K,sigma,theta) returns
the mean of and variance for the generalized Pareto (GP) distribution
with the tail index (shape) parameter K, scale
parameter sigma, and threshold (location) parameter, theta.
The default value for theta is 0.
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 the Pareto distribution. 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,
.
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.
See Also
gppdf, gpcdf, gpinv, gpfit, gplike, gprnd
 | gprnd | | growTrees (TreeBagger) |  |
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