TESTING THE FIT TO GENERALIZED POISSON DISTRIBUTIONS BASED ON AN EMPIRICAL TRANSFORM

Abstract

Generalized Poisson distributions appear as applied-research models in many fields. For example in reliability, the total amount of wear of items, the hazard rate and the total time to failure can be modeled after a Generalized Poisson distribution. Methods of Statistical Inference for such distributions have been scarce since the corresponding distribution functions come in complicated, often not closed form, expressions. In this article, we present a method for testing the goodness-of-fit to any specified member of the family of Generalized Poisson distributions. The proposed method utilizes the general form of the moment generating function of Generalized Poisson distributions. The asymptotic distribution of the test statistics is derived when the parameters of the generalizing distribution are assumed known as well as unknown. The performance of the procedures is investigated by employing real and simulated data.