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

Abstract

In this paper, we define and discuss $\mathcal{R}(p,q)$- deformations of basic univariate discrete distributions of the probability theory. We mainly focus on binomial, Euler, Pólya and inverse Pólya distributions. We discuss relevant $\mathcal{R}(p,q)-$ 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.