In probability theory and statistics, the Beta distribution is a family of continuous probability distributions defined on the interval [0,1] parametrized by two non-negative shape parameters, typically denoted by alpha and beta.

f(x,alpha,beta) =   (x^(alpha-1)*(1-x)^(beta-1))/B(alpha,beta)

The beta function, B\Beta, is a normalization constant to ensure that the total probability is 1.

where   beta(z,w) = integral from 0 to 1 of t^(z-1)(1-t)^(w-1) dt.

support 0 ⇐ x ⇐ 1