Calculation
Even if unavailable directly, the complete and incomplete Beta function values can be calculated using functions commonly included in spreadsheet or Computer algebra systems. With Excel as an example, using the GammaLn and (cumulative) Beta distribution functions, we have:
- Complete Beta Value = Exp(GammaLn(a) + GammaLn(b) - GammaLn(a + b))
and,
- Incomplete Beta Value = BetaDist(x, a, b) * Exp(GammaLn(a) + GammaLn(b) - GammaLn(a + b)).
These result from rearranging the formulae for the Beta distribution, and the incomplete beta and complete beta functions, which can also be defined as the ratio of the logs as above.
Similarly, in MATLAB and GNU Octave, betainc (Incomplete beta function) computes the regularized incomplete beta function - which is, in fact, the Cumulative Beta distribution - and so, to get the actual incomplete beta function, one must multiply the result of betainc by the result returned by the corresponding beta function.
Read more about this topic: Beta Function
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