The New Explanation of Lomax Distribution: Its Properties, Inference, and Applications to Real-Life Data

Abstract

This paper introduces an extended form of the Lomax model known as the new extended heavy-tailed Lomax (NEHTLx) distribution. The NEHTLx distribution features a failure rate that can exhibit various shapes, including unimodal, bathtub, reversed-J, and decreasing patterns. This versatility means that the failure rate function can have multiple peaks, making it potentially more suitable for fitting a wide range of data. The probability density function of the NEHTLx can be expressed as a combination of Lomax densities. The paper explores several mathematical properties of the NEHTLx distribution using various statistical tools. It also employs classical analytical methods to estimate the parameters of the NEHTLx model. To assess the performance of these estimation methods, comprehensive simulations are conducted for both small and large datasets. The ranking of these methods is analyzed using partial and overall ranks to evaluate their effectiveness. Additionally, the paper highlights the advantages of the NEHTLx distribution compared to traditional Lomax distributions through an analysis of two real-world datasets from applied domains, demonstrating its practical relevance and superior fitting capabilities.