Extreme Value Distribution

(continuous probab. dist. for equations)

Usage:

ExtremeValueDist (x, α, β)

Definition:

 exp (-exp (-(x-α)/β) - (x-α)/β) / β

Parameters:

α = location        β = scale

Required:

β > 0

Moments:

μ = α + γ β       (γ = Eulers = 0.5772156649)

σ = πβ / sqrt(6)

γ1 = 1.3          β2 = 5.4

This distribution is the limiting distribution for the smallest or largest values in large samples drawn from a variety of distributions, including the normal distribution.

Also known as the "Fisher-Tippet distribution", "Fisher-Tippet Type I distribution" or the "log-Weibull distribution".