Computation of bivariate gamma and inverted beta distribution functions

Abstract

This paper considers the evaluation of the distribution functions of the bivariate gamma distribution of Wicksell and Kibble, and a bivariate inverted beta distribution. Simple expansions of the distribution functions in terms of marginal quantities and the negative binomial probabilities are derived.

Keywords:

• Wicksell-Kibble bivariate gamma
• correlated bivariate inverted beta
• negative binomial distribution
• error bounds
• computer generation of random variates