The Modified Borel–Tanner (Mbt) Regression Model

Abstract

A new one-parameter family of discrete distributions is presented. It has some advantages against the Poisson distribution as a suitable model for modelling data with a high frequencies of zeros and showing over-dispersion (variance larger than the mean). The distribution is obtained from a simple modification of the Borel–Tanner distribution, which has not received attention from the statistical community in the past. We also propose a generalized regression model which can be used for a count dependent variable, when the above features are observed, as an alternative to the well-known Poisson regression model, among others. Maximum likelihood estimation is investigated and illustrated with an example of interrelation between fatalities in trucks accidents on American roads and some covariates considered.