A Note on the Spinned Poisson Distribution

Abstract

Recently a new probability distribution, the spinned Poisson distribution (SPD), was introduced to model data collected in various health management situations, such as the spread of an infectious disease when infected cases are removed from the observed population. As the name suggests, the SPD is a generalization of the well known Poisson distribution. In this paper, simple data sets are used to show that there is no guarantee that the equations for the maximum likelihood estimates of the parameters associated with the SPD have a nontrivial solution. It follows that even for a simple data set where a nontrivial SPD may seem appropriate, the fitted SPD may be just a Poisson distribution.