On the hyper-dirichlet type 1 and hyper-liouville distributions

Abstract

This paper concerns the characterization of a new family of multivariate beta distribution functions - the hyper-Dirichlet type 1 distribution. This family describes the joint density function of the terminal variates of an arbitrary tree constructed from finite sequences of probability vectors having independent Dirichlet type 1 distributions. Expressions for the general properties of the hyper-Dirichlet type 1 distribution are presented. In addition, the hyper-Liouville distribution is described and its properties are discussed as well as a generalization of the Liouville integral identity.

Keywords:

• Beta-Liouville distribution
• Dirichlet type 1 distribution
• generalized Dirichlet distribution
• hyper-beta Liouville distribution
• random proportions
• sequence
• tree