Generalized Dirichlet Distribution Based on Confluent Hypergeometric Series

Abstract

Dirichlet distribution is a kind of high-dimensional continuous probability distribution, which has important applications in the fields of statistics, machine learning and bioinformatics. In this paper, based on gamma distribution we study two two-dimensional random variables. Then we derive the properties of these two two-dimensional random variables by using the properties of non-central gamma distribution and confluent hypergeometric series. From these properties, we find the two random variables follow generalized Dirichlet distributions. Applying hypergeometric series to Dirichlet distribution broadens the research of Dirichlet distribution.