The Poisson Inverse Pareto Distribution and Its Application

Abstract

This paper proposes a new combination of the inverse Pareto distribution as a three-parameter distribution—the Poisson inverse Pareto distribution—derived from the concept of a unified model for long-term survival analyses. This work derives the proposed distribution’s probability properties, including the survival, cumulative distribution, probability density, and hazard functions. Moreover, some properties of the Poisson inverse Pareto distribution are presented, such as the value-at-risk, tail behavior, quantile function, and order statistics. The maximum likelihood estimation is then studied to obtain a parameter estimation. This study’s simulation revealed that the estimated parameter’s mean-squared errors decreased when the sample size increased. Finally, this work illustrates the Poisson inverse Pareto distribution’s application using two real datasets to demonstrate that the proposed distribution provides a superior fit to that of other models.