The Confluent Hypergeometric Beta Distribution

Saralees Nadarajah () and Malick Kebe
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Saralees Nadarajah: Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
Malick Kebe: Department of Mathematics, Howard University, Washington, DC 20059, USA

Mathematics, 2023, vol. 11, issue 9, 1-23

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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