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Engen's extended negative binomial model revisited

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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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Authors and Affiliations

  1. Faculty of Economics, Kanazawa University, Kakuma-machi, 920-1192, Kanazawa-shi, Ishikawa, Japan

    Nobuaki Hoshino

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  1. Nobuaki Hoshino
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Hoshino, N. Engen's extended negative binomial model revisited. Ann Inst Stat Math 57, 369–387 (2005). https://doi.org/10.1007/BF02507030

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  • DOI: https://doi.org/10.1007/BF02507030

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