Beta Distribution

(continuous probability dist for equations)

Usage:

BetaDist (x, α, β)

Definition:

 x^(α-1) (1-x)^(β-1) / beta (α, β)

 where beta is the beta function

Required:

α > 0        β > 0

Support:

0 ⋜ x ⋜ 1

Moments:

μ = α / (α + β)

σ^2 = α β / [(α + β)^2 (α + β + 1)]

γ1 = 2 (β – α) sqrt((α+β+1) / (αβ)) / (α+β+2)

β2 = 3 (α+β+1)[2(α+β)^2 + αβ(α+β-6)] / [αβ(α+β+2)(α+β+3)]