Advances of the Zero Truncated and Zero Inflated/Adjusted Discrete Models in Count Data Analyses

In fields of sociology, psychology, ecology, insurance, medicine and epidemiology, count data are often collected for specific studies. While count data without zero-category or with excess zeros arise quite frequently, a series of zero-truncated and zero-inflated models were soon developed to analyze these kinds of data, such as zero-truncated/inflated Poisson distribution and zero-truncated/inflated negative binomial distribution. It is necessary to make statistical inferences on unknown parameters when fitting data by these models. Existing studies merely focus on one of these models. In this paper, based on the stochastic representations of zero-truncated and zero-inflated distributions proposed in recent years, we construct a general method to obtain the maximum likelihood estimates of parameters under a unified framework, and make a review on familiar discrete distributions. Moreover, zero-adjusted models are further proposed to extend the applications, aiming to provide researchers appropriate and convenient methods in count data analyses. All methods are demonstrated by simulation studies and two real data analyses.