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### How do I calculate values of the beta function?

 Title Calculating the beta function Author Nicholas J. Cox, Durham University, UK Date November 2001

The beta function can be defined in terms of the gamma function and thus, calculated using the Stata functions exp() and lngamma(). On the latter, see the section "Mathematical functions" of the [D] Functions. Given arguments a and b, the beta function

        Β(a,b) = Γ(a) Γ(b) / Γ(a + b)


can be calculated from


exp(lngamma(a) + lngamma(b) - lngamma(a + b))


In this expression, each argument may be a number, a variable, or, more generally, itself an expression.