SUT J. Math. 58 (2), 117-155, (December 2022) DOI: 10.55937/sut/1670473255
KEYWORDS: Rp,q-calculus, quantum algebras, multinomial coefficient, multivariate Vandermonde formula, multivariate Pólya distribution, multivariate hypergeometric distribution, Bivariate distribution, Rp,q-factorial moments, Rp,q-covariance, 17B37, 81R50, 60E05, 05A30
We construct the multivariate probability distributions (Pólya, inverse Pólya, hypergeometric and negative hypergeometric) from the generalized quantum deformed algebras. Moreover, we derive the corresponding bivariate probability distributions and determine their properties (-factorial moments and covariance). Besides, we deduce particular cases of probability distributions from the quantum algebras known in the literature.