Bivariate Double Inflated Poisson Model And Its Application

There are a large number of paired data in the research of various fields of society,which has profound significance for its reasonable description and exploration of overall information.If the unary regression model is used to fit the count data that appears,the overall information cannot be fully utilized.This results in a large deviation in parameter estimation.At this time,the data can be fitted by establishing a binary Poisson regression model.When a large number of paired count data appear at 0 points,it is called a binary zero expansion phenomenon.Research in recent years It is found that,in addition to a large number of pairs of data appearing at(0,0)points,they also appear at(1,1)points,which is called the dual dual expansion phenomenon.So a reasonable study of the dual dual expansion model is The significance of this paper.This article can be divided into two parts: The first part is extended to the general form of the binary double-expansion Poisson distribution and the binary double-expansion Poisson distribution based on a single mixing parameter through the binary Poisson distribution,and discusses the binary double-expansion Poisson distribution Properties.Then two methods of parameter estimation are introduced: moment estimation method and maximum likelihood estimation method.Then numerical simulation is performed to obtain the mean square error of each parameter under the two estimation methods,and the maximum likelihood estimation fitting is found by comparison.The effect is more ideal than the fitting effect of the moment estimation method.When the number of samples is larger,the mean square error of each parameter under the two estimation methods is smaller.Finally,through an example analysis,it is found that the general form of the binary double expansion Poisson distribution ratio contains a single mixed parameter The binary double-expansion Poisson distribution can more accurately describe the overall information.In the second part,in order to verify whether the count data appearing in pairs meets the binary double-expansion Poisson model,each parameter needs to be tested.In this paper,the Score test method is used to test the inflation parameter and the covariance parameter respectively,and then numerical simulation is used to test the power of the model.Finally,the dual double inflation Poisson model is used to fit the U.S.medical survey data to verify that the dual double inflation Poisson model has research value and significance.