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Derivatives of the Incomplete Beta Function

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  • Boik, Robert J.
  • Robinson-Cox, James F.

Abstract

The incomplete beta function is defined as where Beta(p, q) is the beta function. Dutka (1981) gave a history of the development and numerical evaluation of this function. In this article, an algorithm for computing first and second derivatives of Ix,p,q with respect to p and q is described. The algorithm is useful, for example, when fitting parameters to a censored beta, truncated beta, or a truncated beta-binomial model.

Suggested Citation

  • Boik, Robert J. & Robinson-Cox, James F., 1998. "Derivatives of the Incomplete Beta Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 3(i01).
    • Handle: RePEc:jss:jstsof:v:003:i01
    DOI: http://hdl.handle.net/10.18637/jss.v003.i01
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    References listed on IDEAS

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    1. Ram Tripathi & Ramesh Gupta & John Gurland, 1994. "Estimation of parameters in the beta binomial model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 317-331, June.
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    1. Cadot, Olivier & Roller, Lars-Hendrik & Stephan, Andreas, 2006. "Contribution to productivity or pork barrel? The two faces of infrastructure investment," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1133-1153, August.
    2. Pi, Jinxiu & Yang, Guanghui & Tang, Wei & Yang, Hui, 2022. "Stochastically stable equilibria for evolutionary snowdrift games with time costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    3. Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.
    4. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    5. Xiang, Qinfang & Edwards, Jode & Gadbury, Gary L., 2006. "Interval estimation in a finite mixture model: Modeling P-values in multiple testing applications," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 570-586, November.

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