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Accurate Numerical Computation of the Beta PDF

Authored by: Eduardo A. Brizuela, Willem Deconinck, Chris Lacor

brizuela.jpgCorresponding Author:
Name: Eduardo A. Brizuela
Affiliation:  Department of Mechanical Engineering

University of La Plata
Buenos Aires, Argentina.

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The authors of this paper deal with specific aspects of the modelling of turbulent diffusion flames where the Beta probability distribution is used. The unique aspect of this paper is that the author shows that the traditional problems of over-flow and under-flow can be avoided using their unique method of calculation for certain limiting conditions.

Key Words: Beta PDF, numerical computation

The computation of the Beta PDF is discussed and algorithms are described which permit calculation of the PDF over the full range of its parameters without recourse to approximations or polynomial expansions. This is achieved by giving simple rules for the treatment of the trivial cases and a new algorithm for the general cases, particularly for the cases where the PDF becomes infinity at the extremes of the range. The problems of underflow and overflow when performing the calculations on a digital computer are also addressed, and a general prescaling procedure is presented which overcomes these problems. It is shown that the new algorithms perform more efficiently than commercial mathematical packages.

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