A bivariate beta distribution

The Dirichlet distribution is often used as a prior distribution for the parameters of a multinomial distribution. Because this distribution has support on the simplex 0 less than or equal to x(i) less than or equal to 1, Sigmax(i) = 1, it does not serve as the prior for a correlated binomial distribution. We here present a bivariate beta distribution that has support on 0 less than or equal to x(i) less than or equal to 1, i = 1, 2. When expanded in a power series it is related to the hypergeometric function. This bivariate density is positively likelihood ratio dependent and hence is positive quadrant dependent. (C) 2003 Elsevier Science B.V. All rights reserved.