Zero-inflated model

Demography

Statistical inference

Statistics

Overdispersion

Count data

Applied mathematics

Poisson distribution

Distribution (mathematics)

Regression analysis

Regression

Mathematics

Econometrics

Population

Sociology

Mathematical analysis

Empirical distribution function

Poisson regression

Applied Mathematical Modelling

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.

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