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An EM algorithm for multivariate Poisson distribution and related models

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  • Dimitris Karlis

Abstract

Multivariate extensions of the Poisson distribution are plausible models for multivariate discrete data. The lack of estimation and inferential procedures reduces the applicability of such models. In this paper, an EM algorithm for Maximum Likelihood estimation of the parameters of the Multivariate Poisson distribution is described. The algorithm is based on the multivariate reduction technique that generates the Multivariate Poisson distribution. Illustrative examples are also provided. Extension to other models, generated via multivariate reduction, is discussed.

Suggested Citation

  • Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:1:p:63-77
    DOI: 10.1080/0266476022000018510
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    Cited by:

    1. Bora Çekyay & J.B.G. Frenk & Sonya Javadi, 2023. "On Computing the Multivariate Poisson Probability Distribution," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-22, September.
    2. Emily B. Dennis & Byron J.T. Morgan & Martin S. Ridout, 2015. "Computational aspects of N-mixture models," Biometrics, The International Biometric Society, vol. 71(1), pages 237-246, March.
    3. Kalema, George & Molenberghs, Geert, 2016. "Generating Correlated and/or Overdispersed Count Data: A SAS Implementation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(c01).
    4. Chan, Jennifer So Kuen & Wan, Wai Yin, 2014. "Multivariate generalized Poisson geometric process model with scale mixtures of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 72-87.
    5. Rolf Larsson, 2020. "Discrete factor analysis using a dependent Poisson model," Computational Statistics, Springer, vol. 35(3), pages 1133-1152, September.
    6. Vicente G. Cancho & Dipak K. Dey & Francisco Louzada, 2016. "Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 572-584, March.
    7. Tom Brijs & Dimitris Karlis & Filip Van den Bossche & Geert Wets, 2007. "A Bayesian model for ranking hazardous road sites," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 1001-1017, October.
    8. Su Pei-Fang & Mau Yu-Lin & Li Chung-I & Guo Yan & Liu Qi & Shyr Yu & Boice John D., 2017. "Bivariate Poisson models with varying offsets: an application to the paired mitochondrial DNA dataset," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(1), pages 47-58, March.
    9. Yang, Ying & Kang, Jian, 2010. "Joint analysis of mixed Poisson and continuous longitudinal data with nonignorable missing values," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 193-207, January.
    10. Lillestøl, Jostein, 2020. "Sampling risk evaluations in a tax fraud case: Some modelling issues," Discussion Papers 2020/5, Norwegian School of Economics, Department of Business and Management Science.
    11. Rolf Larsson, 2022. "Bartlett correction of an independence test in a multivariate Poisson model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 391-417, November.
    12. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
    13. Wenqiong Xue & Jian Kang & F. DuBois Bowman & Tor D. Wager & Jian Guo, 2014. "Identifying functional co-activation patterns in neuroimaging studies via poisson graphical models," Biometrics, The International Biometric Society, vol. 70(4), pages 812-822, December.
    14. Guo-Liang Tian & Xiqian Ding & Yin Liu & Man-Lai Tang, 2019. "Some new statistical methods for a class of zero-truncated discrete distributions with applications," Computational Statistics, Springer, vol. 34(3), pages 1393-1426, September.
    15. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2016. "Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 63-78.
    16. Sobom M. Somé & Célestin C. Kokonendji & Nawel Belaid & Smail Adjabi & Rahma Abid, 2023. "Bayesian local bandwidths in a flexible semiparametric kernel estimation for multivariate count data with diagnostics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 843-865, September.
    17. 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.
    18. Robert C. Jung & Andrew R. Tremayne, 2020. "Maximum-Likelihood Estimation in a Special Integer Autoregressive Model," Econometrics, MDPI, vol. 8(2), pages 1-15, June.

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