Beta Distribution |
(continuous probability dist for equations) |
Usage: |
BetaDist (x, a, b) |
Definition: |
x^(a-1) (1-x)^(b-1) / beta (a, b) where beta is the beta function |
Required: |
a > 0 b > 0 |
Support: |
0 £ x £ 1 |
Moments: |
m = a / (a + b) s^2 = a b / [(a + b)^2 (a + b + 1)] g1 = 2 (b – a) sqrt((a+b+1) / (ab)) / (a+b+2) b2 = 3 (a+b+1)[2(a+b)^2 + ab(a+b-6)] / [ab(a+b+2)(a+b+3)] |
Almost any reasonably smooth unimodal distribution on [0,1] can 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.