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

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.