Open Access

ARTICLE

On a Novel Extended Lomax Distribution with Asymmetric Properties and Its Statistical Applications

by Aisha Fayomi¹, Christophe Chesneau^2,*, Farrukh Jamal³, Ali Algarni¹

1 Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
2 Université de Caen Normandie, LMNO, Campus II, Science 3, Caen, 14032, France
3 Department of Statistics, the Islamia University of Bahawalpur, Punjab, 63100, Pakistan

* Corresponding Author: Christophe Chesneau. Email:

Computer Modeling in Engineering & Sciences 2023, 136(3), 2371-2403. https://doi.org/10.32604/cmes.2023.027000

Received 08 October 2022; Accepted 02 December 2022; Issue published 09 March 2023

Abstract

In this article, we highlight a new three-parameter heavy-tailed lifetime distribution that aims to extend the modeling possibilities of the Lomax distribution. It is called the extended Lomax distribution. The considered distribution naturally appears as the distribution of a transformation of a random variable following the logweighted power distribution recently introduced for percentage or proportion data analysis purposes. As a result, its cumulative distribution has the same functional basis as that of the Lomax distribution, but with a novel special logarithmic term depending on several parameters. The modulation of this logarithmic term reveals new types of asymetrical shapes, implying a modeling horizon beyond that of the Lomax distribution. In the first part, we examine several of its mathematical properties, such as the shapes of the related probability and hazard rate functions; stochastic comparisons; manageable expansions for various moments; and quantile properties. In particular, based on the quantile functions, various actuarial measures are discussed. In the second part, the distribution’s applicability is investigated with the use of the maximum likelihood estimation method. The behavior of the obtained parameter estimates is validated by a simulation work. Insurance claim data are analyzed. We show that the proposed distribution outperforms eight well-known distributions, including the Lomax distribution and several extended Lomax distributions. In addition, we demonstrate that it gives preferable inferences from these competitor distributions in terms of risk measures.

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Keywords

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