A Generalized Inflated Poisson Distribution with Application to Modeling Fertility Data

Abstract

The standard Poisson distribution, which is widely used to model count data, may not provide a good fit to model women’s fertility (defined as the number of children per woman in her lifetime) in a specific population due to various cultural and sociological reasons. Therefore, the usual Poisson distribution is inflated at specific values suitably, as dictated by the societal norms, to fit the available data. In this paper we first discuss an inflated Poisson distribution in general terms (called Generalized Inflated Poisson), and then consider special cases of it to fit fertility data from Sweden.