An overview of goodness-of-fit tests for the Poisson distribution

The Poisson distribution has a large number of applications and is often used as a model in both a practical and a theoretical setting. As a result, various goodness-of-fit tests have been developed for this distribution. In this paper, we compare the finite sample power performance of ten of these tests against a wide range of alternative distributions for various sample sizes. The alternatives considered include, seemingly for the first time, weighted Poisson distributions. A number of additional tests are of historical importance although their power performance is not competitive against the remaining tests. These tests are discussed, but their powers are not included in the numerical analysis. The Monte Carlo study presented below indicates that the test with the best overall power performance is the test of Meintanis and Nikitin (2008), followed closely by the test of Rayner and Best (1990) (originally studied in Fisher, 1950