BRATIO

Algorithm 708: Significant digit computation of the incomplete beta function ratios. An algorithm is given for evaluating the incomplete beta function ratio Ix(a,b) and its complement 1 - Ix(a,b). A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

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References in zbMATH (referenced in 10 articles , 2 standard articles )

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  1. Li, Junlin; Wang, Tongke; Hao, Yonghong: The series expansions and Gauss-Legendre rule for computing arbitrary derivatives of the beta-type functions (2020)
  2. Gil, A.; Segura, J.; Temme, N. M.: Efficient algorithms for the inversion of the cumulative central beta distribution (2017)
  3. Bregman, Robert L.: A heuristic procedure for solving the dynamic probabilistic project expediting problem (2009)
  4. L’Ecuyer, Pierre; Simard, Richard J.: Inverting the symmetrical beta distribution. (2006)
  5. Smith, David M.: Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions (2001)
  6. Brown, Barry W.; Spears, Floyd M.; Levy, Lawrence B.; Lovato, James; Russell, Kathy: Algorithm 762: LLDRLF, log-likelihood and some derivatives for log-(F) models (1996)
  7. Doman, B. G. S.: An asymptotic expansion for the incomplete beta function (1996)
  8. Brown, B. W.; Levy, L. B.: Certification of algorithm 708: Significant-digit computation of the incomplete beta function ratios (1994)
  9. Lozier, D. W.; Olver, F. W. J.: Numerical evaluation of special functions (1994)
  10. DiDonato, Armido R.; Morris, Alfred H. jun.: Algorithm 708: Significant digit computation of the incomplete beta function ratios (1992)