Abstract
The ConwayMaxwellPoisson (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 wellknown 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 

Pages (fromto)  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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Fraser A. Daly
 School of Mathematical & Computer Sciences  Associate Professor
 School of Mathematical & Computer Sciences, Actuarial Mathematics & Statistics  Associate Professor
Person: Academic (Research & Teaching)