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The Confluent Hypergeometric Beta Distribution

Author

Listed:
  • Saralees Nadarajah

    (Department of Mathematics, University of Manchester, Manchester M13 9PL, UK)

  • Malick Kebe

    (Department of Mathematics, Howard University, Washington, DC 20059, USA)

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.

Suggested Citation

  • Saralees Nadarajah & Malick Kebe, 2023. "The Confluent Hypergeometric Beta Distribution," Mathematics, MDPI, vol. 11(9), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2169-:d:1139732
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    References listed on IDEAS

    as
    1. Gordy, Michael B, 1998. "Computationally Convenient Distributional Assumptions for Common-Value Auctions," Computational Economics, Springer;Society for Computational Economics, vol. 12(1), pages 61-78, August.
    2. Yingbo Li & Merlise A. Clyde, 2018. "Mixtures of g-Priors in Generalized Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1828-1845, October.
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