Beta Function

The beta function forms part of the definition of several distributions:

It is convenient to define the beta function in terms of the gamma function:

The graph below shows the range of values of the Beta function for the values of a and b used in the documentation for the Beta distribution.

Spreadsheets

Excel does not have a dedicated Beta function, however, it is possible to use the gammaln function which returns the log (to base e) of the gamma function, thus values beta function can be obtained using this formula:

beta(a,b) = exp(gammaln(a)+gammaln(b)-gammaln(a+b))

Programming Languages

The beta and gammaln functions are not usually present in the math libraries of general purpose programming languages, however, maybe available in specialist libraries which the application can access.  This site has the code for an implementation of the gammaln function based on the Stirling series.

Page Modified: 20-Jun-2008

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