G. W. Cran, K. J. Martin, G. E. Thomas, Remark AS R19 and Algorithm AS 109: A Remark on Algorithms: AS 63: The Incomplete Beta Integral AS 64: Inverse of the Incomplete Beta Function Ratio, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 26, No. 1 (1977), pp. 111-114
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Cran et al. (1977) studied this question.
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