Open Access
ARTICLE
On a Novel Extended Lomax Distribution with Asymmetric Properties and Its Statistical Applications
Aisha Fayomi1, Christophe Chesneau2,*, 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.
Keywords
Cite This Article
Fayomi, A., Chesneau, C., Jamal, F., Algarni, A. (2023). On a Novel Extended Lomax Distribution with Asymmetric Properties and Its Statistical Applications.
CMES-Computer Modeling in Engineering & Sciences, 136(3), 2371–2403.