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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 univ...

An increasingly popular approach to model the dependence between random variables centers on the use of copula functions. Herein, a score test for testing independence of response variables using the Normal copula function is proposed for the specific case, where the marginal distributions are known to be Poisson; to our knowledge, this approach to testing independence is unique to this article. The simulation study shows the test that keeps the significance level close to the nominal one. Similarly, the estimated significance level and power of the likelihood ratio and Wald tests are also compared to show our test is numerically stable and superior in very small samples. A real-world dataset is used to demonstrate the application of our test.