Method For Generating Bivariate Poisson Variable With Negative Correlation

Poisson distribution takes an important role in research and real-world applica-tions. In many cases, people need to product multivariate Poisson variable, especially the binary Poisson variable, whose parameters and correlation matrix are predeter-mined.The problem has been well solved when the correlation coefficient is positive. However, when it’s negative, methods such as NOTRA and Inbal’s method, can only get approximate result and got high computational complexity on the same time.The present paper create two new methods:Bernoulli-Poisson and Bernoulli-Poisson-Iteration to solve this problem.Bernoulli-Poisson can product binary Poisson variable whose parameters and cor-relation coefficient are predetermined. The correlation coefficient is a negative number contained in a predetermined interval.When the predetermined correlation coefficient is out of the interval, this paper propose another method called Bernoulli-Poisson-Iteration. In the process, I acquire some useful results. For example, you can get the result of max very simple calculation, where X, Y are two arbitrary discrete variables.