Statistics and Its Interface

Volume 10 (2017)

Number 2

Type I multivariate zero-inflated generalized Poisson distribution with applications

Pages: 291 – 311

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n2.a12

Authors

Xi-Fen Huang (Department of Statistics and Actuarial Science, University of Hong Kong)

Guo-Liang Tian (Department of Mathematics, South University of Science and Technology of China, Shenzhen, Guangdong, China)

Chi Zhang (Department of Statistics and Actuarial Science, University of Hong Kong )

Xuejun Jiang (Department of Mathematics, South University of Science and Technology of China, Shenzhen, Guangdong, China)

Abstract

Excessive zeros in multivariate count data are often encountered in practice. Since the Poisson distribution only possesses the property of equi-dispersion, the existing Type I multivariate zero-inflated Poisson distribution (Liu and Tian, 2015, CSDA) cannot be used to model multivariate zero-inflated count data with over-dispersion or under-dispersion. In this paper, we extend the univariate zero-inflated generalized Poisson (ZIGP) distribution to Type I multivariate ZIGP distribution via stochastic representation aiming to model positively correlated multivariate zero-inflated count data with over-dispersion or underdispersion. Its distributional theories and associated properties are derived. Due to the complexity of the ZIGP model, we provide four useful algorithms (a very fast Fisher-scoring algorithm, an expectation/conditional-maximization algorithm, a simple EM algorithm and an explicit majorization– minimization algorithm) for finding maximum likelihood estimates of parameters of interest and develop efficient statistical inference methods for the proposed model. Simulation studies for investigating the accuracy of point estimates and confidence interval estimates and comparing the likelihood ratio test with the score test are conducted. Under both AIC and BIC, our analyses of the two data sets show that Type I multivariate ZIGP model is superior over Type I multivariate zero-inflated Poisson model.

Keywords

AIC, BIC, EM algorithm, Fisher scoring algorithm, MM algorithm, multivariate zero-inflated generalized Poisson distribution, zero-inflated count data

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