Statistical Analysis Of Bivariate Doubly Inflated Poisson Model

When performing statistical observation,the bivariate Poisson(BP)distribution provides a useful model for investigating paired count data.Situations can arise where count data exhibit inflated rates of zeros,that is,a phenomenon known as zero-inflated bivariate.In fact,the bivariate zero-inflated Poisson regression model(BZIP)has been widely used in many aspects such as finance,insurance,and medicine.Many pairs of count data contain a large number of kk),(points in addition to a large number of zero points.This phenomenon is called bivariate double inflation.Based on the BZIP model,this paper establishes a bivariate doubly inflated Poisson model(BDIP),discusses some distribution properties of the BDIP model,and performs a score test for testing inflated parameters and covariance parameter.In this paper,based on the existing BP distribution and BZIP distribution,the BDIP distribution is proposed,and the BDIP distribution properties are discussed.The moment estimation and maximum likelihood estimation are used to estimate the parameters.The fitting effect of the new model is verified by numerical simulation and case analysis,and the fitting effect of the maximum likelihood estimation is better than that of the moment estimation.The BDIP regression model was proposed by BP regression model and BZIP regression model.In order to evaluate whether the paired count data conformed to the BDIP regression model,testing the two inflated parameters and the covariance parameter,and the score test for testing covariance parameter is better,but the score test for testing inflated parameters are slightly worse.And the power of testing a single inflated parameter is better than testing two inflated parameters at the same time.The analysis shows that the number of patients visiting doctors and the number of prescription drugs prescribed by doctors are suitable for BDIP model.Therefore,BDIP model has research significance and practical value.