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A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data

Author

Listed:
  • Seng Huat Ong

    (Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia
    Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia)

  • Shin Zhu Sim

    (School of Mathematical Sciences, University of Nottingham Malaysia, Semenyih 43500, Malaysia)

  • Shuangzhe Liu

    (Faculty of Science and Technology, University of Canberra, Bruce, ACT 2617, Australia)

  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan)

Abstract

This paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture structure adds flexibility and facilitates application and use in analysis. The family of distributions is exemplified using a mixture of negative binomial and shifted negative binomial distributions. Some basic and probabilistic properties are derived. We perform hypothesis testing for equi-dispersion and simulation studies of their power and consider parameter estimation via maximum likelihood and probability-generating-function-based methods. The utility of the distributions is illustrated via their application to real biological data sets exhibiting under-, equi- and over-dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM–Poisson distributions for handling under-, equi- and over-dispersion in count data.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:3:p:59-955:d:1242517
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    References listed on IDEAS

    as
    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.
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    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. Kimberly F. Sellers & Stephen J. Peng & Ali Arab, 2020. "A Flexible Univariate Autoregressive Time‐Series Model for Dispersed Count Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(3), pages 436-453, May.
    6. Dexter Cahoy & Elvira Di Nardo & Federico Polito, 2021. "Flexible models for overdispersed and underdispersed count data," Statistical Papers, Springer, vol. 62(6), pages 2969-2990, December.
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    9. S. Chakraborty & S. H. Ong, 2016. "A COM-Poisson-type generalization of the negative binomial distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(14), pages 4117-4135, July.
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