Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution

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Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution

TitleGeneralized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution
Publication TypeJournal Article
Year of Publication2005
AuthorsJoe, H, Zhu, R
JournalBiometrical Journal
Volume47
Pagination219-229
Date PublishedAPR
ISSN0323-3847
AbstractWe prove that the generalized Poisson distribution GP(theta, eta) (eta >= 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.
DOI10.1002/bimj.200410102