Detecting departures from a poisson model

Abstract

Poisson models can be widely used for analyzing count data and belong to some broad classes of discrete distributions such as a Katz family, a double exponential family and a family of discrete distributions with a finite first moment. Several procedures for testing goodness of fit of a Poisson model against these classes are discussed and simulations are conducted to compare their performance for detecting departures from Poisson models.

Keywords:

• Poisson model
• katz family
• double exponential family
• probability generating function
• overdispersion
• underdispersion