Bivariate distributions based on the generalized three-parameter beta distribution

The generalized three-parameter beta distribution with pdf proportional to Xa-1(1-x)(b-1)/{1- (1-lambda)x}(a+b) is a flexible extension of the classical beta distribution with interesting applications in statistics. In this chapter, several bivariate extensions of this distribution are studied. We propose models with given marginals: a first model consists of a transformation with monotonic components of the Dirichlet distribution and a second model that uses the bivariate Sarmanov-Lee distribution. Next, the class of distributions whose conditionals belong to the generalized three-parameter beta distribution is considered. Two important subfamilies are studied in detail. The first one contains as a particular case the models of Libby and Novick (1982) and Olkin and Liu (2003). The second family is more general, and contains among others, the model proposed by Arnold, Castillo and Sarabia (1999). In addition, using two different conditional schemes, we study conditional survival models. Multivariate extensions are also discussed. Finally, an application to Bayesian analysis is given.