@article{Mustafa2025, 
author = {Abdelfattah Mustafa and M. I. Khan and Samah M. Ahmed},
title = {Estimating the stress-strength reliability parameter of the inverse power Lomax distribution},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {15632-15652},
keywords = {maximum likelihood estimator, the inverse power Lomax model, stress-strength reliability, symmetric and asymmetric loss functions, bootstrap resampling, Bayes estimator},
url = {https://www.sciopen.com/article/10.3934/math.2025700},
doi = {10.3934/math.2025700},
abstract = {This research focused on estimating the stress-strength parameter by considering stress and strength as distinct random variables, both characterized by the inverse power Lomax (IPL) distribution. The maximum likelihood estimate (MLE) for stress-strength reliability was then calculated using the Newton-Raphson method. Using the asymptotic normality of MLEs, this study developed approximate confidence intervals. Bootstrap confidence intervals for the stress-strength reliability parameter (   R) were investigated. The Bayes estimator of    R was considered. Furthermore, we utilized the Markov chain Monte Carlo (MCMC) method to create both symmetric and asymmetric loss functions, allowing for a more comprehensive analysis. The highest posterior density (HPD) credible intervals under a gamma prior distribution were calculated. The different approaches were assessed using a Monte Carlo simulation. Finally, a numerical example was given to show the effectiveness of the proposed methods.}
}