- Beta Distribution

The probability density function (pdf) of a beta random variable with shape parameters a and b is given by

f(x|a, b) = 1 B(a, b)

xa−1(1− x)b−1, 0 < x < 1, a > 0, b > 0,

where the beta function

B(a, b) = Γ(a)Γ(b)

Γ(a+ b) .