A Note on Discrete Degenerate Random Variables

Taekyun Kim; Dae San Kim; Lee-Chae Jang; H. Y. Kim

Working Paper Article Version 1 This version is not peer-reviewed

Version 1 : Received: 14 November 2019 / Approved: 15 November 2019 / Online: 15 November 2019 (16:43:03 CET)

In this paper, we introduce two discrete degenerate random variables, namely the degenerate binomial and degenerate Poisson random variables. We deduce the expectations of the degenerate binomial random variables. We compute the generating function of the moments of the degenerate Poisson random variables, which leads us to define the new type degenerate Bell polynomials, and hence obtain explicit expressions for the moments of those random variables in terms of such polynomials. We also get the variances of the degenerate Poisson random variables. Finally, we illustrate two examples of the degenerate Poisson random variables.

discrete degenerate random variables; degenerate binomial random variable; degenerate Poisson random variable; new type degenerate Bell polynomials

Computer Science and Mathematics, Discrete Mathematics and Combinatorics

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A Note on Discrete Degenerate Random Variables

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