Some Structural Properties Related to the Borel-Taner Distribution and its’ Application

Abstract

The Borel-Tanner distribution, with two shape parameters, and r, has some leverage over the Poisson distribution, other mixtures of the Poisson distribution, and several other discrete distributions, as it can be applied to both under and over-dispersed count data. In this article, some structural properties are studied that have not been explored earlier including recursive relation between successive probabilities. For illustrative purposes, two real-life data sets will be considered to show the applicability of this distribution that are re-analyzed for this purpose.