Generalization of Generalized Beta Distributions

摘要

This paper introduces the compound confluent hypergeometric (CCH) distribution.211u001eThe CCH unifies and generalizes three recently introduced generalizations of the 211u001ebeta distribution: the Gauss hypergeometric (GH) distribution of Armero and 211u001eBayarri (1994), the generalized beta (GB) distribution of McDonald and Xu (1995), 211u001eand the confluent hypergeometric (CH) distribution of Gordy (forthcoming). In 211u001eaddition to greater flexibility in fitting data, the CCH offers two useful 211u001eproperties. Unlike the beta, GB and GH, the CCH allows for conditioning on 211u001eexplanatory variables in a natural and convenient way.The CCH family is conjugate 211u001efor gamma distributed signals, and so may also prove useful in Bayesian analysis. 211u001eApplication of the CCH is demonstrated with two measures of household liquid 211u001eassets. In each case, the CCH yields a statistically significant improvement in 211u001efit over the more restrictive alternatives.