R(p,q)- analogs of discrete distributions: general formalism and application

In this paper, we define and discuss $\mathcal{R}(p,q)$- 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 $\mathcal{R}(p,q)-$ 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 $q-$ Quesne quantum algebra, used in physics. Other known results in the literature are also recovered as particular cases

Multinomial Probability Distribution and Quantum Deformed Algebras

An examination is conducted on the multinomial coefficients derived from generalized quantum deformed algebras, and on their recurrence relations. The R(p, q)-deformed multinomial probability distribution and the negative R(p, q)-deformed multinomial probability distribution are constructed, and the recurrence relations are determined. From our general result, we deduce particular cases that correspond to quantum algebras considered in the literature

Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra

In this paper, we construct the Heisenberg-Virasoro algebra in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Moreover, the $\mathcal{R}(p,q)$-Heisenberg-Witt $n$-algebras is also investigated. Furthermore, we generalize the notion of the elliptic hermitian matrix models. We use the constraints to evaluate the $\mathcal{R}(p,q)$-differential operators of the Virasoro algebra and generalize it to higher order differential operators. Particular cases corresponding to quantum algebras existing in literature are deduced

Multi-parameter Fermi-Dirac and Bose-Einstein Stochastic Distributions

In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties, namely ($\mathcal{R}(p,q)$-mean, $\mathcal{R}(p,q)$-variance and $\mathcal{R}(p,q)$-covariance) are computed and discussed. Particular cases corresponding to quantum algebras existing in literature are deduced