A flexible novel extended lomax model for capturing complex patterns in engineering data sets

Due to the complexity of real data, there is a growing need for new distributions. Introducing new models enables us to refine this data and stay current with the times. In this paper, a new flexible distribution, called the new extended Lomax distribution, is proposed. The properties of the proposed model are thoroughly derived, including kurtosis and order statistics, among others. The suggested distribution supports various hazard rate functions, including decreasing, reversed J-shaped, and unimodal forms. Additionally, it can fit positively skewed data with leptokurtic behavior in both dispersion and over-dispersion scenarios. The Bayesian and classical approaches, including maximum likelihood, ordinary least squares, and Bayes estimators under various loss functions, are used for parameter estimation. The effectiveness of the proposed distribution is demonstrated through a simulation study, which shows that the Bayes estimator based on the squared error loss function produces more accurate parameter estimates than alternative methods. Furthermore, several actuarial measures were computed. A simulation study utilizing these actuarial metrics was subsequently conducted. Two engineering data sets are used to further evaluate the goodness-of-fit of the suggested model, demonstrating competitive performance compared to other fitting models.