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.

incomplete beta function, inversion methods
Computation of special functions, construction of tables (msc 65D20)
Software (theme 1)
Numerical Algorithms
Accepted for publication; DOI: 10.1007/s11075-016-0139-2

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.