A note on goodness of fit testing for the Poisson distribution

Abstract: Since its introduction in 1950, Fisher's dispersion test has become a standard means of deciding whether or not count data follow the Poisson distribution. The test is based on a characteristic property of the Poisson distribution, and discriminates well between the Poisson and the natural alternative hypotheses of binomial and negative binomial distributions. While the test is commonly used to test for general deviations from Poissonity, its performance against more general alternatives has not been widely investigated. This paper presents realistic alternative hypotheses for which general goodness of fit tests perform much better than the Fisher dispersion test.