An accurate and efficient algorithm for the inversion of the cumulative central beta distribution ratios is described. The algorithm is based on the combination of the Schwarzian-Newton method and asymptotic inversion methods when the parameters are large.

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Numerical Algorithms

Gil, A, Segura, J, & Temme, N.M. (2017). Efficient algorithms for the inversion of the cumulative central beta distribution. Numerical Algorithms, 74(1), 77–91.