ABSTRACT
In this section the most general bivariate densities with Gordy gener alized beta conditionals are derived. The model (VIII. 1), in addition to including, as a particular case, the classic beta, also includes three important existing models:
where and denotes the Gauss hypergeo metric function. The GH gives to the ordinary beta if either
• Confluent Hypergeometric (Gordy, 1998a). Making v = 1 and 0 = 1 , the CCH(p, q ,r,s,u = 1,0 = 1) simplifies to the con fluent distribution CH(p, q, s) with pdf:
and, for each
These are beta conditional densities. It is not difficult (using the Stephanos-Levi-Civita-Suto theorem again) to verify that the corre sponding joint survival function must be of the form:
f o r O < x < l , 0 < y < 1 where a ,b ,c> 0. Note that these models could also be viewed as having proportional conditional hazard func tions.
