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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Infinite divisibility of the Whittaker distribution
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by Genet M. Assefa and Árpád Baricz;
Proc. Amer. Math. Soc. 151 (2023), 5429-5442
DOI: https://doi.org/10.1090/proc/16562
Published electronically: September 1, 2023

Abstract:

In this paper, by using an integral representation of Ismail and Kelker for the quotient of Tricomi hypergeometric functions, we investigate the infinite divisibility and self-decomposability of the recently defined four-parameter lifetime Whittaker distribution, which is a natural extension of the classical gamma, exponential, chi-square, generalized Lindley, Lindley, beta prime, and Lomax distributions. We also show that the Whittaker distribution belongs to the class of hyperbolically completely monotone distributions and generalized gamma convolutions, and it is a super-Gaussian distribution. By using some results for the moments of the Whittaker distribution, we also deduce some Turán type inequalities for the Whittaker functions of the second kind and as an application we show that the effective variance of the Whittaker distribution is bounded from below.
References
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Bibliographic Information
  • Genet M. Assefa
  • Affiliation: Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
  • Email: genetmekonnen428@gmail.com
  • Árpád Baricz
  • Affiliation: Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania; and Institute of Applied Mathematics, Óbuda University, 1034 Budapest, Hungary
  • MR Author ID: 729952
  • Email: bariczocsi@yahoo.com
  • Received by editor(s): March 21, 2023
  • Received by editor(s) in revised form: May 22, 2023
  • Published electronically: September 1, 2023

  • Dedicated: Á. Baricz dedicates this paper to the memory of his parents Teréz and Árpád
  • Communicated by: Mourad Ismail
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 5429-5442
  • MSC (2020): Primary 60E07; Secondary 33C15
  • DOI: https://doi.org/10.1090/proc/16562
  • MathSciNet review: 4648937