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

@article{Joe2005GeneralizedPD,
  title={Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution.},
  author={Harry Joe and Ruiyue Zhu},
  journal={Biometrical journal. Biometrische Zeitschrift},
  year={2005},
  volume={47 2},
  pages={
          219-29
        }
}
We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 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… CONTINUE READING
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