A note on a test for Poisson overdispersion

Abstract

SUMMARY This note discusses an error occurring in a test for Poisson overdispersion suggested by Tiago de Oliveira (1965). The limiting null distribution of the suggested statistic is neither pivotal nor is it standard normal. The error lies in the computation of the asymptotic standard error of the overdispersion estimate, for which a corrected version is given. The corrected version of the test statistic becomes equivalent to the normalized version of Fisher's index of dispersion.