Properties and inference of the Pareto Lomax distribution with applications to real data

Abstract

This paper introduces a new four-parameter lifetime model, the odd Pareto–Lomax (OPLx) distribution. By extending the Lomax model, the OPLx distribution provides enhanced flexibility for modeling real-world data across various fields. It accommodates a range of failure rate shapes, including decreasing, unimodal, increasing, J-shaped, and reversed-J-shaped. The paper outlines key properties of the OPLx model and employs eight different estimation methods to estimate its parameters. These methods are essential for developing guidelines on selecting the most effective estimation approach. Detailed simulation studies are conducted to evaluate the performance of the proposed estimators, using partial and overall ranks across various parametric combinations. The practical utility and versatility of the OPLx distribution are further demonstrated through the analysis of three real-world datasets, revealing that the OPLx model offers superior flexibility and outperforms other competing Lomax models.