Multinomial probability distribution and quantum deformed algebras

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.