The beta distribution (the term first used by Gini, 1911) is defined as:

f(x) = G(n+w)/(G(n)G(w)) * xn-1* (1-x)w-1

0 < x < 1, n > 0, w > 0

where

G (gamma) |
is the gamma function |

n, w |
are the shape parameters |

The animation above shows the beta distribution as the two shape parameters change. For a complete listing of all distributions, see Distribution and Their Functions.