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A bivariate beta distribution

Author

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  • Olkin, Ingram
  • Liu, Ruixue

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.

Suggested Citation

  • Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:4:p:407-412
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