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

Abstract

The Borel-Tanner distribution, with two shape parameters, $\alpha ,$ 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.

KEYWORDS AND PHRASES:

• Borel-Tanner distribution
• recursive relation
• stochastic ordering
• maximum likelihood estimation
• earthquake data
• federalist data

Acknowledgments

Both the authors acknowledge the fact that the results are derived independently and this research is currently submitted to this journal only.

Authors’ Contributions

The first author worked on the simulation and application part while the second author has worked on the structural properties part.

Data Availability Statement

All the data sets utilized in this manuscript are available on the specific references made freely.