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A flexible distribution class for count data

Author

Listed:
  • Kimberly F. Sellers

    (Georgetown University)

  • Andrew W. Swift

    (University of Nebraska - Omaha)

  • Kimberly S. Weems

    (North Carolina Central University)

Abstract

The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-parameter generalization of the Poisson distribution that can accommodate data over- or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this model’s flexibility, encompassing several classical distributions as well as other count data distributions containing significant data dispersion.

Suggested Citation

  • Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "A flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-21, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0077-0
    DOI: 10.1186/s40488-017-0077-0
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    References listed on IDEAS

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    1. Sharad Borle & Utpal M. Dholakia & Siddharth S. Singh & Robert A. Westbrook, 2007. "The Impact of Survey Participation on Subsequent Customer Behavior: An Empirical Investigation," Marketing Science, INFORMS, vol. 26(5), pages 711-726, 09-10.
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    8. Joseph B. Kadane & Ramayya Krishnan & Galit Shmueli, 2006. "A Data Disclosure Policy for Count Data Based on the COM-Poisson Distribution," Management Science, INFORMS, vol. 52(10), pages 1610-1617, October.
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    Cited by:

    1. Kimberly F. Sellers & Tong Li & Yixuan Wu & Narayanaswamy Balakrishnan, 2021. "A Flexible Multivariate Distribution for Correlated Count Data," Stats, MDPI, vol. 4(2), pages 1-19, April.
    2. 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).
    3. 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.
    4. 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).
    5. Kimberly F. Sellers & Ali Arab & Sean Melville & Fanyu Cui, 2021. "A flexible univariate moving average time-series model for dispersed count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-12, December.

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