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The incomplete beta function and its ratio to the complete beta function

Authors: David Osborn and Richard Madey
Journal: Math. Comp. 22 (1968), 159-162
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Abstract | References | Additional Information

Abstract: The incomplete beta function, $ {B_x}(p,q) = \int {_0^x} {y^{p - 1}}{(1 - y)^{q - 1}}dy$, and its ratio to the complete beta function $ {B_1}(p,q)$ has been calculated on an IBM-7044 computer to five significant figures and tabulated for the arguments p and q each in the interval from 0.5 to 2.0 with increments of 0.05 and for the parameter $ x$ in the interval 0.1 to 1.0 with increments of 0.01. The function was evaluated by first expanding a factor of the integrand in a binomial series and then integrating each term. In order to facilitate computation, one expansion is taken for $ x \leqq 1/2$ and another for $ 1/2 < x \leqq 1$. The expansions are truncated when the relative error is less than or equal to an arbitrarily predetermined fraction. Typical running time for achieving five significant figures on the IBM-7044 is about one minute for $ {10^4}$ values.

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Additional Information

Article copyright: © Copyright 1968 American Mathematical Society