Bivariate Distributions Based on the Generalized Three-Parameter Beta Distribution

  • José María Sarabia
  • Enrique Castillo
Part of the Statistics for Industry and Technology book series (SIT)


The generalized three-parameter beta distribution with pdf proportional to x a−1(1−x)b−1/{1−(1−λ)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 (1982) and (2003). The second family is more general, and contains among others, the model proposed by (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.

Keywords and phrases:

Generalized three-parameter beta distribution Gauss hypergeometric distribution Dirichlet and Sarmanov-Lee distributions conditionally specified models 


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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • José María Sarabia
    • 1
  • Enrique Castillo
    • 1
  1. 1.University of CantabriaSantanderSpain

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