refs.bib

@article{berry_1990,
 title = {Algorithm AS R83: A Remark on Algorithm AS 109: Inverse of the Incomplete Beta Function Ratio},
 ISSN = {00359254, 14679876},
 URL = {http://www.jstor.org/stable/2347779},
 author = {K. J. Berry and P. W. Mielke and G. W. Cran},
 journal = {Journal of the Royal Statistical Society. Series C (Applied Statistics)},
 number = {2},
 pages = {309--310},
 publisher = {Royal Statistical Society, Oxford University Press},
 volume = {39},
 year = {1990}
}

@article{blair_1976,
  title = {Rational Chebyshev Approximations for the Inverse of the Error Function},
  author = {Blair, J. M. and Edwards, C. A. and Johnson, J. H.},
  date = {1976},
  year = {1976},
  journal = {Mathematics of Computation},
  shortjournal = {Math. Comp.},
  volume = {30},
  number = {136},
  pages = {827--830},
  issn = {0025-5718, 1088-6842},
  doi = {10.1090/S0025-5718-1976-0421040-7},
  url = {https://www.ams.org/mcom/1976-30-136/S0025-5718-1976-0421040-7/},
  langid = {english}
}

@article{brent_1978,
  title = {A Fortran Multiple-Precision Arithmetic Package},
  author = {Brent, Richard P.},
  date = {1978-03},
  year = {1978},
  journal = {ACM Transactions on Mathematical Software},
  shortjournal = {ACM Trans. Math. Softw.},
  volume = {4},
  number = {1},
  pages = {57--70},
  issn = {0098-3500, 1557-7295},
  doi = {10.1145/355769.355775},
  url = {https://dl.acm.org/doi/10.1145/355769.355775},
  langid = {english}
}

@article{cran_1977,
 title = {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},
 author = {Cran, G. W. and Martin, K. J. and Thomas, G. E.},
 journal = {Journal of the Royal Statistical Society. Series C (Applied Statistics)},
 number = {1},
 issn = {00359254, 14679876},
 url = {http://www.jstor.org/stable/2346887},
 pages = {111--114},
 publisher = {Royal Statistical Society, Oxford University Press},
 volume = {26},
 year = {1977}
}

@article{chattamvelli_1997,
  title = {Computing the Non-Central Beta Distribution Function},
  author = {Chattamvelli, R. and Shanmugam, F.},
  date = {1997-03-01},
  year = {1997},
  journal = {Journal of the Royal Statistical Society Series C: Applied Statistics},
  volume = {46},
  number = {1},
  pages = {146--156},
  issn = {0035-9254, 1467-9876},
  doi = {10.1111/1467-9876.00055},
  url = {https://academic.oup.com/jrsssc/article/46/1/146/6990591},
  langid = {english}
}

@article{didonato_1986,
    title = {Computation of the incomplete gamma function ratios and their inverse},
    author = {DiDonato, Armido R and Morris, Alfred H},
    volume = {12},
    issn = {0098-3500, 1557-7295},
    url = {https://dl.acm.org/doi/10.1145/22721.23109},
    doi = {10.1145/22721.23109},
    abstract = {An algorithm is given for computing the incomplete gamma function ratios $P(a, x)$ and $Q(a, x)$ for $a \geq 0$, $x \geq 0$, $a + x \neq 0$. Temme's uniform asymptotic expansions are used. The algorithm is robust; results accurate to 14 significant digits can be obtained. An' extensive set of coefficients for the Temme expansions is included. An algorithm, employing third-order Schröder iteration supported by Newton-Raphson iteration, is provided for computing $x$ when $a$, $P(a, x)$, and $Q(a, x)$ are given. Three iterations at most are required to obtain 10 significant digit accuracy for $x$.},
    language = {en},
    number = {4},
    urldate = {2025-03-08},
    journal = {ACM Transactions on Mathematical Software},
    month = dec,
    year = {1986},
    pages = {377--393},
}


@article{didonato_1992,
  title = {Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios},
  shorttitle = {Algorithm 708},
  author = {Didonato, Armido R. and Morris, Alfred H.},
  date = {1992-09},
  year = {1992},
  journal = {ACM Transactions on Mathematical Software},
  shortjournal = {ACM Trans. Math. Softw.},
  volume = {18},
  number = {3},
  pages = {360--373},
  issn = {0098-3500, 1557-7295},
  doi = {10.1145/131766.131776},
  url = {https://dl.acm.org/doi/10.1145/131766.131776},
  langid = {english}
}

@article{fukushima_2009,
  title = {Fast Computation of Complete Elliptic Integrals and Jacobian Elliptic Functions},
  author = {Fukushima, Toshio},
  date = {2009-12},
  year = {2009},
  journal = {Celestial Mechanics and Dynamical Astronomy},
  shortjournal = {Celest. Mech. Dyn. Astr.},
  volume = {105},
  number = {4},
  pages = {305--328},
  issn = {0923-2958, 1572-9478},
  doi = {10.1007/s10569-009-9228-z},
  url = {http://link.springer.com/10.1007/s10569-009-9228-z},
  langid = {english}
}

@article{fukushima_2015,
  title = {Precise and Fast Computation of Complete Elliptic Integrals by Piecewise Minimax Rational Function Approximation},
  author = {Fukushima, Toshio},
  date = {2015-07},
  year = {2015},
  journal = {Journal of Computational and Applied Mathematics},
  volume = {282},
  pages = {71--76},
  issn = {03770427},
  doi = {10.1016/j.cam.2014.12.038},
  url = {https://www.sciencedirect.com/science/article/pii/S0377042715000023},
  langid = {english}
}

@article{lenth_1987,
  title = {Algorithm AS 226: Computing Noncentral Beta Probabilities},
  shorttitle = {Algorithm AS 226},
  author = {Lenth, Russell V.},
  date = {1987},
  year = {1987},
  journal = {Applied Statistics},
  volume = {36},
  number = {2},
  eprint = {10.2307/2347558},
  eprinttype = {jstor},
  pages = {241},
  issn = {00359254},
  doi = {10.2307/2347558},
  url = {https://www.jstor.org/stable/10.2307/2347558?origin=crossref},
  urldate = {2025-02-19}
}

@article{macleod_1996,
  title = {Rational Approximations, Software and Test Methods for Sine and Cosine Integrals},
  author = {MacLeod, Allan J.},
  date = {1996-09},
  year = {1996},
  journal = {Numerical Algorithms},
  shortjournal = {Numer. Algor.},
  volume = {12},
  number = {2},
  pages = {259--272},
  issn = {1017-1398, 1572-9265},
  doi = {10.1007/BF02142806},
  url = {http://link.springer.com/10.1007/BF02142806},
  langid = {english}
}