The Beta distribution reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Beta distribution

In probability theory and statistics, the beta distribution is a continuous probability distribution with the probability density function defined on the interval [0, 1]:

where a and b are parameters that must be greater than zero.

When the "constant" is included explicitly, the density looks like this:

where Γ and B are respectively the gamma function and the beta function.

The special case of the beta distribution, when a = 1 and b = 1, is the standard uniform distribution.

The expected value and variance of a beta random variable X with parameters a and b are given by the formulae:

On the other hand, with the expected value and variance of a beta random variable X given, the parameters a and b are calculated by the formulae:

where 0 < E(X) < 1 and 0 < var(X) < E(X) (1 − E(X)).

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