Abstract
The present article shows that a limiting argument that is essentially the law of small numbers produces a proper discrete multivariate distribution from any generalized Poisson distribution. Based on this result, Engen's Extended Negative Binomial (ENB) model is derived from the Poisson-Pascal distribution, which is a generalization of the inverse Gaussian-Poisson distribution. The ENB model is also derived from Sichel's generalized inverse Gaussian-Poisson distribution. The application of the ENB model is discussed thereto.
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