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Uniformly most powerful unbiased tests for the dispersion parameter of the Conway–Maxwell–Poisson distribution

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  • Bedbur, S.
  • Kamps, U.

Abstract

Uniformly most powerful unbiased tests for one-sided hypotheses about the dispersion parameter of the Conway–Maxwell–Poisson distribution are derived by utilizing the exponential family structure, and it is shown how to obtain the critical values of the relevant test statistics via simulation. The tests, which do not require parameter estimators, are applied to several real data sets from the literature to statistically confirm under- or overdispersion, giving evidence against the common Poisson model for count data.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:196:y:2023:i:c:s0167715223000251
    DOI: 10.1016/j.spl.2023.109801
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    References listed on IDEAS

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    1. 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.
    2. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "Correction to: a flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-1, December.
    3. Olatunde Adebayo Adeoti & Jean-Claude Malela-Majika & Sandile Charles Shongwe & Muhammad Aslam, 2022. "A homogeneously weighted moving average control chart for Conway–Maxwell Poisson distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(12), pages 3090-3119, September.
    4. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    5. Ramesh Gupta & S. Sim & S. Ong, 2014. "Analysis of discrete data by Conway–Maxwell Poisson distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 327-343, October.
    6. 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.
    7. A. Huang & A. S. I. Kim, 2021. "Bayesian Conway–Maxwell–Poisson regression models for overdispersed and underdispersed counts," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(13), pages 3094-3105, July.
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