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Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference

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  • Sellers, Kimberly F.
  • Morris, Darcy Steeg
  • Balakrishnan, Narayanaswamy

Abstract

The bivariate Poisson distribution is a popular distribution for modeling bivariate count data. Its basic assumptions and marginal equi-dispersion, however, may prove limiting in some contexts. To allow for data dispersion, we develop here a bivariate Conway–Maxwell–Poisson (COM–Poisson) distribution that includes the bivariate Poisson, bivariate Bernoulli, and bivariate geometric distributions all as special cases. As a result, the bivariate COM–Poisson distribution serves as a flexible alternative and unifying framework for modeling bivariate count data, especially in the presence of data dispersion.

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  • Sellers, Kimberly F. & Morris, Darcy Steeg & Balakrishnan, Narayanaswamy, 2016. "Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 152-168.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:152-168
    DOI: 10.1016/j.jmva.2016.04.007
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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. Minkova, Leda D. & Balakrishnan, N., 2014. "Type II bivariate Pólya–Aeppli distribution," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 40-49.
    3. Balakrishnan, N. & Pal, Suvra, 2013. "Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 41-67.
    4. Felix Famoye & P. Consul, 1995. "Bivariate generalized Poisson distribution with some applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 127-138, December.
    5. Sun, Kai & Basu, Asit P., 1995. "A characterization of a bivariate geometric distribution," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 307-311, June.
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    Cited by:

    1. Yuvraj Sunecher & Naushad Mamode Khan & Vandna Jowaheer & Marcelo Bourguignon & Mohammad Arashi, 2019. "A Primer on a Flexible Bivariate Time Series Model for Analyzing First and Second Half Football Goal Scores: The Case of the Big 3 London Rivals in the EPL," Annals of Data Science, Springer, vol. 6(3), pages 531-548, September.
    2. 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.
    3. 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.
    4. Rufin Bidounga & Evrand Giles Brunel Mandangui Maloumbi & Réolie Foxie Mizélé Kitoti & Dominique Mizère, 2020. "The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(6), pages 1-1, November.
    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. Mamode Khan Naushad & Rumjaun Wasseem & Sunecher Yuvraj & Jowaheer Vandna, 2017. "Computing with bivariate COM-Poisson model under different copulas," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 131-146, June.
    7. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    8. Juliana Schulz & Christian Genest & Mhamed Mesfioui, 2021. "A multivariate Poisson model based on comonotonic shocks," International Statistical Review, International Statistical Institute, vol. 89(2), pages 323-348, August.

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