The score test for independence of two marginal Poisson variables

Abstract

We propose a score test for testing independence of the marginals based on Lakshminarayana’s bivariate Poisson probability mass function. Each marginal distribution of the bivariate model is a univariate Poisson distribution, and the parameters of the bivariate distribution can be estimated using maximum likelihood methods. The simulation study shows that the score test maintains size close to the nominal level. To assess the efficiency of the derived score test, the estimated significance levels and powers of the likelihood ratio and Wald tests as well as Spearman’s rank correlation test are calculated and compared. A relevant dataset is used to illustrate the application of the bivariate Poisson model and the proposed score test for independence.