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.

One useful descriptive metric for measuring variability in applied statistics is the coefficient of variation (CV) of a distribution. However, it is uncommon to report conclusions about the CV of non-normal distributions. This study develops a method for estimating the CV for the inverse power Lomax (IPL) distribution using adaptive Type-Ⅱ progressive censored data. The experiment is a well-liked plan for gathering data, particularly for a very dependable product. The point and interval estimate of CV are formulated under the classical approach (maximum likelihood and bootstrap) and the Bayesian approach with respect to the symmetric loss function. For the unknown parameters, the joint prior density is calculated using the Bayesian technique as a product of three independent gamma densities. Additionally, it is recommended to use the Markov Chain Monte Carlo (MCMC) method to calculate the Bayes estimate and generate posterior distributions. A simulation study and a numerical example are given to assess the performance of the maximum likelihood and Bayes estimations.