Multinomial probability distribution and quantum deformed algebras

TL;DR

This paper explores the mathematical structure of multinomial distributions within the framework of quantum deformed algebras, deriving recurrence relations and special cases relevant to quantum algebra literature.

Contribution

It introduces a new $ ext{R}(p,q)$-deformed multinomial probability distribution and its negative form, expanding the understanding of quantum algebra applications in probability theory.

Findings

Derived recurrence relations for deformed multinomial coefficients

Constructed $ ext{R}(p,q)$-deformed multinomial distributions

Connected results to existing quantum algebra literature

Abstract

The multinomial coefficient and their recurrence relations from the generalized quantum deformed algebras are examined. Moreover, the $\mathcal{R}(p,q)-$ deformed multinomial probability distribution and the negative $\mathcal{R}(p,q)-$ deformed multinomial probability distribution are constructed. The recurrence relations are also determined. Particular cases of our results corresponding to the quantum algebras in the literature are deduced from the general formalism.