Construction of a new multivariate Poisson distribution through the conditional probability with its variance covariance matrix: application to the simulation of Poisson regressions

摘要

In this study, we construct a new multivariate Poisson distribution. This new law is the product of the conditional univariate Poisson distribution. So we determine its variance covariance matrix. Through the parameters of Poisson distribution, we construct k-models of Poisson regression. We carry out their estmation and hypothesis tests related to it. As the bivariate datas were studied a lot, we want to realize an application of the trivariate case.