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
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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
- 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
Dedicated: Á. Baricz dedicates this paper to the memory of his parents Teréz and Árpád