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Conjugate Analysis of the Conway-Maxwell-Poisson Distribution
journal contribution
posted on 2008-07-01, 00:00 authored by Joseph B. Kadane, Galit Shmueli, Thomas P. Minka, Sharad Borle, Peter BoatwrightPeter BoatwrightThis article explores a Bayesian analysis of a generalization of the
Poisson distribution. By choice of a second parameter v, both under-dispersed
and over-dispersed data can be modeled. The Conway-Maxwell-Poisson distribution forms an exponential family of distributions, so it has sufficient statistics of
fixed dimension as the sample size varies, and a conjugate family of prior distributions. The article displays and proves a necessary and sufficient condition on the
hyperparameters of the conjugate family for the prior to be proper, and it discusses
methods of sampling from the conjugate distribution. An elicitation program to
find the hyperparameters from the predictive distribution is also discussed.