Score Test For Zero-and-K Inflated Poisson Model

The counting data model has always been the focus and hotspot of attention in statistics.It has a wide range of applications.However,in the processing of actual data,there will be too many cases of Zero or K,and it is impossible to solve such data with the traditional counting model.At this time,we choose to use the 0-inflated or k-inflated model for fitting;in the medical and other fields,there are often 0 and 1 large-scale data models,and then use the Zero-and-One inflated model to do the fitting.In fact,in some cases,there may be a large number of Zero and K in the count data,and then the Zero-and-K inflated model needs to be used for fitting.In this paper,the 0-inflated Poisson model and the k-inflated Poisson model are extended to establish a Zero-and-K inflated Poisson model,and two forms of Zero-and-K inflated Poisson distribution are given.In order to make the model more realistic,the Zero-and-K inflated Poisson regression model with multiple covariates was proposed,and the Zero-and-K inflated Poisson regression model with multiple covariates under two forms are written.Furthermore,this paper continues to study the score test of the Zero-and-K inflated Poisson distribution and the Zero-and-K inflated Poisson regression model to test whether the inflated at the inflated point is to test the 0-k inflated,0-inflated and k-inflated respectively.Two forms of Zero-and-K inflated Poisson distribution and Zero-and-K inflated Poisson regression model are numerically simulated.Through numerical simulation,we can get the power of both forms of Zero-and-K inflated Poisson distribution and Zero-and-K inflated Poisson regression model increase with the increase of sample size;with the increase of inflated coefficient,two kinds of inflated coefficient The power of the Zero-and-K inflated Poisson distribution and the Zero-and-K inflated Poisson regression model are both increased;for test power of the Zero-and-K inflated Poisson distribution and the power of the Zero-and-K inflated Poisson regression model,the second The form’s power is slightly better than the first form of power.