The Confluent Hypergeometric Beta Distribution

Abstract

The confluent hypergeometric beta distribution due to Gordy has been known since the 1990s, but not much of is known in terms of its mathematical properties. In this paper, we provide a comprehensive treatment of mathematical properties of the confluent hypergeometric beta distribution. We derive shape properties of its probability density function and expressions for its cumulative distribution function, hazard rate function, reversed hazard rate function, moment generating function, characteristic function, moments, conditional moments, entropies, and stochastic orderings. We also derive procedures for maximum likelihood estimation and assess their finite sample performance. Most of the derived properties are new. Finally, we illustrate two real data applications of the confluent hypergeometric beta distribution.

Keywords

• confluent hypergeometric function
• maximum likelihood estimation
• moments