Tests For Detecting Overdispersion In Poisson Model

Collings and Margolin(1985) developed a locally most powerful unbiased test for detecting negative binomial departures from a Poisson model, when the variance is a quadratic function of the mean. Kim and Park(1992) developed a locally most powerful unbiased test, when the variance is a linear function of the mean. It is found that a differ ent mean-variance structure of a negative binomial derives a different locally optimal test statistic.In this paper Collings and Margolin's and Kim and Park's results are unified and extended by developing a test for overdispersion in Poisson model against Katz family of distributions. Our setup has two extensions: First, Katz family of distributions is employed as an extension of the negative binomial distribution. Second, the mean-variance structure of the mixed Poisson model is given by sigma(2) = mu + c mu(r) for arbitrary but fixed r. We derive a local score test for testing H-0 : c = 0. Superiority of a new test is proved by the asymptotic relative efficiency as well as the simulation study.