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An Effective Algorithm for the Noncentral Beta Distribution Function

Harry O. Posten
The American Statistician
Vol. 47, No. 2 (May, 1993), pp. 129-131
DOI: 10.2307/2685195
Stable URL: http://www.jstor.org/stable/2685195
Page Count: 3
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An Effective Algorithm for the Noncentral Beta Distribution Function
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Abstract

A simple recursive algorithm is provided for evaluating the noncentral beta distribution function. This algorithm basically reduces the problem to that of evaluating a single central beta distribution function. The algorithm is summarized in a step-by-step form. Since the noncentral F distribution function can be evaluated directly from the noncentral beta distribution function, the algorithm has broad practical use for evaluating the power of analysis of variance and other F tests. The method of this algorithm was used in Lenth. The latter article, however, focuses on a FORTRAN program and on an error bound for the procedure. It does not provide a full development of the procedure. The present article provides a complete development enabling one to readily produce a noncentral beta distribution function program in any desired language, with understanding for each step.

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