R(p,q)- analogs of discrete distributions: general formalism and application
Probability
2019-10-29 v2 Mathematical Physics
math.MP
Abstract
In this paper, we define and discuss - deformations of basic univariate discrete distributions of the probability theory. We mainly focus on binomial, Euler, P\'olya and inverse P\'olya distributions. We discuss relevant 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 Quesne quantum algebra, used in physics. Other known results in the literature are also recovered as particular cases.
Keywords
Cite
@article{arxiv.1901.01840,
title = {R(p,q)- analogs of discrete distributions: general formalism and application},
author = {Mahouton Norbert Hounkonnou and Fridolin Melong},
journal= {arXiv preprint arXiv:1901.01840},
year = {2019}
}