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Derivatives of the Incomplete Beta Function

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

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    Bibliographic Info

    Article provided by American Statistical Association in its journal Journal of Statistical Software.

    Volume (Year): 03 ()
    Issue (Month): i01 ()
    Pages:

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    Handle: RePEc:jss:jstsof:03:i01

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    Web page: http://www.jstatsoft.org/

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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, vol. 46(2), pages 317-331, June.
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    Cited by:
    1. Olivier Cadot & Lars-Hendrik Röller & Andreas Stephan, 2002. "Contribution to Productivity or Pork Barrel? The Two Faces of Infrastructure Investment," CIG Working Papers FS IV 02-09, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    2. Ulf Schepsmeier & Jakob Stöber, 2014. "Derivatives and Fisher information of bivariate copulas," Statistical Papers, Springer, vol. 55(2), pages 525-542, May.

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