The Beta distribution with parameters alpha and beta is denoted by Be(alpha,beta).

The distribution function of the Be(alpha, beta) distribution is denoted by Be(x |alpha,beta).

For example, Be(.5 |1,1)=.5.

The density of the Be(alpha,beta) distribution is

f(x) = B(alpha,beta)^{-1} x^{alpha-1}(1-x)^{beta-1} on the interval (0,1).

Here B(alpha,beta) represents the beta function,
G(alpha)G(beta)/G(alpha+beta),

where G(x) is the gamma function.
The Be(1,1) distribution is the uniform distribution, U(0,1).

The distribution of the kth order statistic of a sample
of size n from the U(0,1) distribution is Be(k,n).