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Analysis of discrete data by Conway–Maxwell Poisson distribution

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  • Ramesh Gupta
  • S. Sim
  • S. Ong

Abstract

In this paper, we further study the Conway–Maxwell Poisson distribution having one more parameter than the Poisson distribution and compare it with the Poisson distribution with respect to some stochastic orderings used in reliability theory. Likelihood ratio test and the score test are developed to test the importance of this additional parameter. Simulation studies are carried out to examine the performance of the two tests. Two examples are presented, one showing overdispersion and the other showing underdispersion, to illustrate the procedure. It is shown that the COM-Poisson model fits better than the generalized Poisson distribution. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:98:y:2014:i:4:p:327-343
    DOI: 10.1007/s10182-014-0226-4
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    References listed on IDEAS

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    1. 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.
    2. Gupta, Pushpa L. & Gupta, Ramesh C. & Tripathi, Ram C., 1996. "Analysis of zero-adjusted count data," Computational Statistics & Data Analysis, Elsevier, vol. 23(2), pages 207-218, December.
    3. Gupta, Ramesh C. & Ong, S. H., 2004. "A new generalization of the negative binomial distribution," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 287-300, March.
    4. Vicente Cancho & Mário Castro & Josemar Rodrigues, 2012. "A Bayesian analysis of the Conway–Maxwell–Poisson cure rate model," Statistical Papers, Springer, vol. 53(1), pages 165-176, February.
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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. Chatla, Suneel Babu & Shmueli, Galit, 2018. "Efficient estimation of COM–Poisson regression and a generalized additive model," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 71-88.
    3. Somayeh Ghorbani Gholiabad & Abbas Moghimbeigi & Javad Faradmal, 2021. "Three-level zero-inflated Conway–Maxwell–Poisson regression model for analyzing dispersed clustered count data with extra zeros," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 415-439, November.
    4. Seyed Ehsan Saffari & John Carson Allen & Robiah Adnan & Seng Huat Ong & Shin Zhu Sim & William Greene, 2019. "Frequency of Visiting a Doctor: A right Truncated Count Regression Model with Excess Zeros," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 9(5), pages 112-122, August.

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