A family of multivariate discrete distributions - Haines, Linda M (South African Statistical Journal, 2020)
In this short paper, the multivariate Poisson-Gamma, the multinomial N-mixture and the negative multinomial distributions are shown to have probability mass functions of the same form and thus to share, broadly, the same distributional properties. The three distributions are, however, fundamentally very different in nature, that is, in terms of genesis, interpretation and model building, and these differences are highlighted and discussed.