Multivariate zero-and-one inflated Poisson model with applications

This paper extends the univariate zero-and-one inflated Poisson (ZOIP) distribution (Melkersson & Olsson, 1999; Zhang et al., 2016) to its multivariate version, which can be used to model correlated multivariate count data with large proportions of zeros and ones marginally. More importantly, this new multivariate ZOIP distribution possesses a flexible dependency structure; i.e., the correlation coefficient between any two random components could be either positive or negative depending on the values of the parameters. The important distributional properties are explored and some useful statistical inference methods without and with covariates are developed. Simulation studies are conducted to evaluate the performance of the proposed methods. Finally, two real data sets on healthcare and insurance are used to illustrate the proposed methods.