  We construct the multivariate probability distributions (P\'olya, inverse
P\'olya, hypergeometric and negative hypergeometric) from the generalized
quantum algebra. Moreover, we derive the bivariate probability distributions
and determine their properties($\mathcal{R}(p,q)$-factorial moments and
covariance). Besides, we deduce particular cases of probability distributions
from the quantum algebras known in the literature.
