### Abstract

The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some well-known models. In this work, we begin by establishing some properties of both the CMP distribution and an analogous generalisation of the binomial distribution, which we refer to as the CMB distribution. We also consider some convergence results and approximations, including a bound on the total variation distance between a CMB distribution and the corresponding CMP limit.

Original language | English |
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Pages (from-to) | 635–658 |

Number of pages | 24 |

Journal | ALEA: Latin American Journal of Probability and Mathematical Statistics |

Volume | 13 |

Issue number | 2 |

Early online date | 31 Jul 2016 |

Publication status | Published - 2016 |

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## Cite this

Daly, F. A., & Gaunt, R. (2016). The Conway-Maxwell-Poisson distribution: Distributional theory and approximation.

*ALEA: Latin American Journal of Probability and Mathematical Statistics*,*13*(2), 635–658.