The Gauss Hypergeometric Beta Distribution

Abstract

The Gauss hypergeometric beta distribution due to Gordy [Computational Economics, 12, 1998, 61-78] has been known since the 1990s.  But not much of is known in terms of its mathematical properties.  In this paper, we pr  ovide a comprehensive treatment of mathematical properties of the Gauss hypergeometric beta distribution.  We derive shape properties of its probability density function and expressions for its cumulative distribution 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 a real data application of the Gauss hypergeometric beta distribution.