Alternative Tests for the Poisson Distribution

Abstract

Poisson distribution is well used as a standard model for analyzing count data. Tests based on the index of dispersion (ID) concerning the variance and the mean are not able to discriminate between the Poisson distribution and some others. An alternative method for the test that data comes from Poisson distribution are proposed based on skewness properties, which is the same as coefficient of variation properties. Monte Carlo studies show that the proposed tests are powerful competitor to the ID tests when alternative distribution is not Poisson but its variance is close to the mean.