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.

Keywords

• Borel-Tanner distribution
• covariate
• estimation