A bivariate beta distribution

Ingram Olkin and Ruixue Liu

Statistics & Probability Letters, 2003, vol. 62, issue 4, 407-412

Abstract: 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-equals, slant]xi[less-than-or-equals, slant]1, [summation operator]xi=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-equals, slant]xi[less-than-or-equals, slant]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.

Keywords: Bayesian; analysis; Dirichlet; distribution; Multinomial; distribution; Hypergeometric; function (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (28)

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