Specification Tests for the Poisson Distribution with a Stochastic Parameter

ABSTRACT

A new method is proposed for testing the mixed Poisson model which employs the well known identity between the probability generating function of the mixed Poisson distribution and the Laplace transform of the mixing distribution. The method utilizes a weighted L2-type statistic which may be easily calculated and the resulting test is consistent against general alternatives. A limit statistic is shown to be related to earlier methods which employ moment-- based contrasts. Some simulation results are also shown.