Score Test Of Zero-and-One Inflated Poisson Model With Semiparametric And Random Effects

When processing statistical data,it is usually encountered that a large number of single values appear.When a large number of Zeros appear in the counting data,it is called Zero inflated phenomenon.When there is a large number of Ones in the counting data,it is called the phenomenon of One inflated.When a large number of Zeros and Ones occur in the counting data at the same time,the phenomenon is called Zero-and-One inflated.The Zero-and-One inflated Poisson distribution provides a very simple and effective model,which is widely used in many research fields,such as insurance,finance,securities,etc.Based on the Zero-and-One inflated Poisson distribution,the Zero-and-One inflated Poisson regression random effect model and the semiparameter Zero-and-One inflated Poisson regression model are established in this paper.The two models were discussed respectively,and the distribution properties of the model were obtained and score test was conducted on the test statistics.This paper is mainly divided into two parts.In the first part,the Zero-and-One inflated Poisson distribution and the Zero-and-One inflated Poisson regression model are summarized by generalization and induction.The random effect vector is introduced on the basis of Zero-and-One inflated regression model,and two kinds of likelihood functions are generated.One is the likelihood function under fixed value,the other is the likelihood function under the value of random effect,derivatives of model parameters and random effect vectors are obtained to test the model.Finally,the experience level of the model is tested by numerical simulation and effect.The second part is based on the log-likelihood function of the Zero-and-One inflated Poisson regression model,the parameter ? of the regression model is concluded and summarized,and introduces a semiparametric model.Using the principle of exponential transformation,the parameter ? is in another form.It can be applied to the likelihood function of the regression model for score test.This part still needs to perform numerical simulation to test the power of the model under the premise of score test.The first two parts need to use the score test method to test the model,so as to determine the distribution nature of the model under specific conditions and the test statistic obeys a specific distribution.