Estimating the stress-strength reliability parameter of the inverse power Lomax distribution

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.