$\mathcal{R}(p,q)$-trinomial probability distribution: properties and particular cases

TL;DR

This paper explores the properties of the $\

Contribution

It introduces a generalized $\\mathcal{R}(p,q)$-trinomial distribution and derives its moments and covariance, extending classical trinomial models.

Findings

Derived $\\mathcal{R}(p,q)$-factorial moments

Computed covariance of the distribution

Identified particular cases from the general formalism

Abstract

In this paper, we investigate the trinomial probability distribution of the first and second kind from the $\mathcal{R}(p,q)$-quantum algebras. Moreover, we compute their $\mathcal{R}(p,q)$-factorial moments and derive the corresponding covariance. Particular cases of trinomial probability distribution are deduced from the formalism developed.