Abstract
In this article, we present a concise review of developments on discrete multivariate distributions. We first present some basic definitions and notations. Then, we present several important discrete multivariate distributions and list their significant properties and characteristics. Keywords: generating function; moments; stirling numbers; regression; inflated distributions; truncated forms; compound distributions; multinomial; negative multinomial; multivariate poisson; multivariate hypergeometric; multivariate Polya–Eggenberger; multivariate discrete exponential; multivariate power series; multivariate hermite; multivariate occupancy; multivariate weighted; dirichlet; multivariate run-related distributions
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