$\mathcal{R}(p,q)$-multivariate discrete probability distributions

TL;DR

This paper introduces a new class of multivariate discrete probability distributions derived from generalized quantum algebra, analyzing their properties and special cases.

Contribution

It constructs multivariate distributions from $ (p,q)$-generalized quantum algebra and explores their factorial moments and covariance.

Findings

Derived multivariate distributions from quantum algebra

Analyzed factorial moments and covariance

Identified particular cases from known quantum algebras

Abstract

We construct the multivariate probability distributions (P\'olya, inverse P\'olya, hypergeometric and negative hypergeometric) from the generalized quantum algebra. Moreover, we derive the bivariate probability distributions and determine their properties($\mathcal{R}(p,q)$-factorial moments and covariance). Besides, we deduce particular cases of probability distributions from the quantum algebras known in the literature.