Speaker: Árpád Baricz, Department of Economics, Babes-Bolyai University, Cluj-Napoca, Romania Institute of Applied Mathematics, Óbuda University, Budapest, Hungary
Title: Infinite divisibility of some distributions related to modified Bessel functions
Abstract: In various real-life situations some concrete models require a random effect to be the sum of several independent random components with the same distribution. In this kind of situation, a very convenient way is to suppose the infinite divisibility of the distribution of these random effects. Similar situations may occur in biology, physics, economics and insurance. In this talk I will focus on continuous univariate probability distributions, like McKay distributions, K-distribution, generalized inverse Gaussian distribution and generalized McKay distributions, which are related to modified Bessel functions of the first and second kinds and in most cases I show that they belong to the class of infinitely divisible distributions, self-decomposable distributions, generalized gamma convolutions and hyperbolically completely monotone densities. Integral representations of quotients of Tricomi hypergeometric functions as well as of quotients of Gaussian hypergeometric functions, or modified Bessel functions of the second kind play an important role in this study. I also deduce a series of new Stieltjes transform representations for products, quotients and their reciprocals concerning modified Bessel functions of the first and second kinds, and I obtain new infinitely divisible modified Bessel distributions with Laplace transforms related to modified Bessel functions of the first and second kind. In addition, I present a new proof via the Pick function characterization theorem for the infinite divisibility of the ratio of two gamma random variables and I present some new Stieltjes transform representations of quotients of Tricomi hypergeometric functions.
The talk is based on the following paper: A. Baricz, D.K. Prabhu, S. Singh, V.A. Vijesh, Infinitely divisible modified Bessel distributions, Constructive Approximation (submitted), https://arxiv.org/abs/2406.17721.
Place: https://ucf.zoom.us/j/94399944324
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