Agricultural and Meteorological Software

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The beta distribution is a family of continuous probability distributions defined on the interval (0, 1) parameterized by two positive shape parameters, typically denoted by α and β. The beta distribution can be suited to the statistical modeling of proportions in applications where values of proportions equal to 0 or 1 do not occur. One theoretical case where the beta distribution arises is as the distribution of the ratio formed by one random variable having a Gamma distribution divided by the sum of it and another independent random variable also having a Gamma distribution with the same scale parameter (but possibly different shape parameter).

References:

Where:

α is the shape parameter

β is the shape parameter

Γ(z) is the gamma function

B is the beta function

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