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)] |
Almost any reasonably smooth unimodal distribution on [0,1] can be approximated by some beta distribution (if its not on [0,1], see Beta4Dist). An important use of the beta distribution is as a conjugate distribution for the parameter of a Bernoulli distribution.
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