Comparing Estimation Methods for the Power–Pareto Distribution

Abstract

Non-negative distributions are important tools in various fields. Given the importance of achieving a good fit, the literature offers hundreds of different models, from the very simple to the highly flexible. In this paper, we consider the power–Pareto model, which is defined by its quantile function. This distribution has three parameters, allowing the model to take different shapes, including symmetrical and left- and right-skewed. We provide different distributional characteristics and discuss parameter estimation. In addition to the already-known Maximum Likelihood and Least Squares of the logarithm of the order statistics estimation methods, we propose several additional methods. A simulation study and an application to two datasets are conducted to illustrate the performance of the estimation methods.

Keywords

• parameter estimation
• power–Pareto distribution
• quantile function