## Abstract

The Conway-Maxwell-Poisson (CMP) distribution is a natural twoparameter

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.

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 (Rio de Janeiro): Latin American journal of probability and mathematical statistics |

Volume | 13 |

Issue number | 2 |

Publication status | Published - 31 Jul 2016 |