R(p,q)- analogs of discrete distributions: general formalism and application

2018/12/27 by Hounkonnou, Mahouton Norbert, Melong, Fridolin
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1901.01840

Abstract

In this paper, we define and discuss R(p,q)- deformations of basic univariate discrete distributions of the probability theory. We mainly focus on binomial, Euler, Pólya and inverse Pólya distributions. We discuss relevant R(p,q)- deformed factorial moments of a random variable, and establish associated expressions of mean and variance. Futhermore, we derive a recursion relation for the probability distributions. Then, we apply the same approach to build main distributional properties characterizing the generalized q- Quesne quantum algebra, used in physics. Other known results in the literature are also recovered as particular cases.

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