Type I multivariate zero-inflated generalized Poisson distribution with applications

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) [15] 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 under dispersion. 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-ihflated Poisson model.