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Type I multivariate zero-inflated Poisson distribution with applications

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  • Liu, Yin
  • Tian, Guo-Liang

Abstract

Motivated from the stochastic representation of the univariate zero-inflated Poisson (ZIP) random variable, the authors propose a multivariate ZIP distribution, called as Type I multivariate ZIP distribution, to model correlated multivariate count data with extra zeros. The distributional theory and associated properties are developed. Maximum likelihood estimates for parameters of interest are obtained by Fisher’s scoring algorithm and the expectation–maximization (EM) algorithm, respectively. Asymptotic and bootstrap confidence intervals of parameters are provided. Likelihood ratio test and score test are derived and are compared via simulation studies. Bayesian methods are also presented if prior information on parameters is available. Two real data sets are used to illustrate the proposed methods. Under both AIC and BIC, our analysis of the two data sets supports the Type I multivariate zero-inflated Poisson model as a much less complex alternative with feasibility to the existing multivariate ZIP models proposed by Li et al. (Technometrics, 29–38, Vol 41, 1999).

Suggested Citation

  • Liu, Yin & Tian, Guo-Liang, 2015. "Type I multivariate zero-inflated Poisson distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 200-222.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:200-222
    DOI: 10.1016/j.csda.2014.10.010
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    References listed on IDEAS

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    1. Bedrick, Edward J. & Hossain, Anwar, 2013. "Conditional tests for homogeneity of zero-inflated Poisson and Poisson-hurdle distributions," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 99-106.
    2. Feng, Ziding & McCulloch, Charles E., 1992. "Statistical inference using maximum likelihood estimation and the generalized likelihood ratio when the true parameter is on the boundary of the parameter space," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 325-332, March.
    3. Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
    4. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    5. Baíllo, A. & Berrendero, J.R. & Cárcamo, J., 2009. "Tests for zero-inflation and overdispersion: A new approach based on the stochastic convex order," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2628-2639, May.
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