# Derivatives of the Incomplete Beta Function

*Robert J. Boik* and
*James F. Robinson-Cox*

*Journal of Statistical Software*, vol. 03, issue i01

**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.

**Date:** 1998-03-15

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