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Computing with bivariate COM-Poisson model under different copulas

Author

Listed:
  • Mamode Khan Naushad

    (University of Mauritius, Reduit, Mauritius)

  • Rumjaun Wasseem

    (University of Mauritius, Reduit, Mauritius)

  • Sunecher Yuvraj

    (University of Technology, Port Louis, Mauritius)

  • Jowaheer Vandna

    (University of Mauritius, Reduit, Mauritius)

Abstract

Bivariate counts are collected in many sectors of research but the analysis of such data is often challenging because each series of counts may exhibit different levels and types of dispersion. This paper addresses this problem by proposing a flexible bivariate COM-Poisson model that may handle any combination of over-, equi- and under-dispersion at any levels. In this paper, the bivariate COM-Poisson is developed via Archimedean copulas. The Generalized Quasi-Likelihood (GQL) approach is used to estimate the unknown mean parameters in the copula-based bivariate COM-Poisson model while the dependence parameter is estimated using the copula likelihood. We further introduce a Monte Carlo experiment to generate bivariate COM-Poisson data under different dispersion levels. The performance of the GQL approach is assessed on the simulated data. The model is applied to analyze real-life epileptic seizures data.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:mcmeap:v:23:y:2017:i:2:p:131-146:n:1
    DOI: 10.1515/mcma-2017-0103
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    1. Siddharth Singh & Sharad Borle & Dipak Jain, 2009. "A generalized framework for estimating customer lifetime value when customer lifetimes are not observed," Quantitative Marketing and Economics (QME), Springer, vol. 7(2), pages 181-205, June.
    2. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    3. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    4. 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.
    5. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    6. Kirthi Kalyanam & Sharad Borle & Peter Boatwright, 2007. "Deconstructing Each Item's Category Contribution," Marketing Science, INFORMS, vol. 26(3), pages 327-341, 05-06.
    7. Siem Jan Koopman & Rutger Lit & André Lucas, 2015. "Intraday Stock Price Dependence using Dynamic Discrete Copula Distributions," Tinbergen Institute Discussion Papers 15-037/III/DSF90, Tinbergen Institute.
    8. 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.
    9. Sharad Borle & Peter Boatwright & Joseph B. Kadane & Joseph C. Nunes & Shmueli Galit, 2005. "The Effect of Product Assortment Changes on Customer Retention," Marketing Science, INFORMS, vol. 24(4), pages 616-622, July.
    10. HEINEN, Andreas & RENGIFO, Erick, 2003. "Multivariate modelling of time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. 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.
    12. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
    13. Boatwright, Peter & Borle, Sharad & Kadane, Joseph B., 2003. "A Model of the Joint Distribution of Purchase Quantity and Timing," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 564-572, January.
    14. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    15. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
    16. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. 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.
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    More about this item

    Keywords

    Bivariate; COM-Poisson; dispersion; GQL; copulas; 65C60; 62J12; 62H12; 62J20; 62J10;
    All these keywords.

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