On the Bell distribution and its associated regression model for count data

Abstract

• We define the one-parameter discrete Bell distribution, which has a simple form for its probability mass function. • It is shown to be a particular solution of a multiple Poisson process. • It is useful for modeling count data with greater variability than the Poisson distribution allows. • We introduce a Bell regression model with statistical inference procedures, diagnostic tools, and computer implementation. • An application to real data suggests that the new model is useful in practice. In this paper we define and study the one-parameter discrete Bell distribution, which has a very simple form for its probability mass function. In particular, we show that this discrete distribution is a particular solution of a multiple Poisson process. By considering the distribution studied in this article, we introduce a new regression model where the response variable is a count. Further, residuals are also proposed for the new count regression model. An empirical application is considered to show the usefulness of the Bell regression model in practice.