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The COM‐Poisson model for count data: a survey of methods and applications

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  • Kimberly F. Sellers
  • Sharad Borle
  • Galit Shmueli

Abstract

The Poisson distribution is a popular distribution for modeling count data, yet it is constrained by its equidispersion assumption, making it less than ideal for modeling real data that often exhibit over‐dispersion or under‐dispersion. The COM‐Poisson distribution is a two‐parameter generalization of the Poisson distribution that allows for a wide range of over‐dispersion and under‐dispersion. It not only generalizes the Poisson distribution but also contains the Bernoulli and geometric distributions as special cases. This distribution's flexibility and special properties have prompted a fast growth of methodological and applied research in various fields. This paper surveys the different COM‐Poisson models that have been published thus far and their applications in areas including marketing, transportation, and biology, among others. Copyright © 2011 John Wiley & Sons, Ltd.

Suggested Citation

  • Kimberly F. Sellers & Sharad Borle & Galit Shmueli, 2012. "The COM‐Poisson model for count data: a survey of methods and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(2), pages 104-116, March.
    • Handle: RePEc:wly:apsmbi:v:28:y:2012:i:2:p:104-116
    DOI: 10.1002/asmb.918
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    Cited by:

    1. Bedbur, S. & Kamps, U., 2023. "Uniformly most powerful unbiased tests for the dispersion parameter of the Conway–Maxwell–Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 196(C).
    2. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    3. Douglas Toledo & Cristiane Akemi Umetsu & Antonio Fernando Monteiro Camargo & Idemauro Antonio Rodrigues Lara, 2022. "Flexible models for non-equidispersed count data: comparative performance of parametric models to deal with underdispersion," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(3), pages 473-497, September.
    4. Seng Huat Ong & Shin Zhu Sim & Shuangzhe Liu & Hari M. Srivastava, 2023. "A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data," Stats, MDPI, vol. 6(3), pages 1-14, September.
    5. Morris, Darcy Steeg & Raim, Andrew M. & Sellers, Kimberly F., 2020. "A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    6. Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).
    7. Muhammed Rasheed Irshad & Sreedeviamma Aswathy & Radhakumari Maya & Saralees Nadarajah, 2023. "New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One," Mathematics, MDPI, vol. 12(1), pages 1-14, December.
    8. Xun-Jian Li & Guo-Liang Tian & Mingqian Zhang & George To Sum Ho & Shuang Li, 2023. "Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms," Mathematics, MDPI, vol. 11(6), pages 1-24, March.

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