Efficient algorithms for the inversion of the cumulative central beta distribution

Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good non-local convergence properties (the Schwarzian-Newton method), asymptotic inversion methods and sharp bounds in the tails of the distribution function.

[1]  Nico M. Temme,et al.  GammaCHI: A package for the inversion and computation of the gamma and chi-square cumulative distribution functions (central and noncentral) , 2015, Comput. Phys. Commun..

[2]  G. E. Thomas,et al.  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 , 1977 .

[3]  Armido R. Didonato,et al.  Algorithm 708: Significant digit computation of the incomplete beta function ratios , 1988, TOMS.

[4]  Javier Segura,et al.  Sharp bounds for cumulative distribution functions , 2015, 1506.03740.

[5]  Robert P. Smith,et al.  Algorithm 724; Program to calculate F-Percentiles , 1993, TOMS.

[6]  Javier Segura,et al.  The Schwarzian-Newton method for solving nonlinear equations, with applications , 2015, Math. Comput..

[7]  K. J. Berry,et al.  Correction to Algorithm AS R83-A Remark on Algorithm AS 109: Inverse of The Incomplete Beta Function Ratio , 1991 .

[8]  Nico M. Temme,et al.  Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios , 2012, SIAM J. Sci. Comput..

[9]  Nico M. Temme,et al.  Asymptotic Methods For Integrals , 2014 .

[10]  G. P. Bhattacharjee,et al.  Inverse of the Incomplete Beta Function Ratio , 1973 .

[11]  Nico M. Temme,et al.  Numerical methods for special functions , 2007 .

[12]  Nico M. Temme.  Asymptotic inversion of the incomplete beta function , 1991 .

[13]  P. Mielke,et al.  A remark on algorithm AS 109 : inverse of the incomplete beta function ratio , 1990 .