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A bivariate beta distribution

✍ Scribed by Ingram Olkin; Ruixue Liu

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
415 KB
Volume
62
Category
Article
ISSN
0167-7152

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✦ Synopsis

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 6 x i 6 1,

x 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 6 x i 6 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.

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