  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.
