Kybernetika 47 no. 1, 15-37, 2011

On the compound Poisson-gamma distribution

Christopher Withers and Saralees Nadarajah


The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.


compound Poisson-gamma, estimation, expansions, moments


62E15, 62E17, 62E20


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