Bayesian estimation for the power rayleigh lifetime model with application under a unified hybrid censoring scheme

This study presents a comprehensive analysis of Bayesian estimation techniques for the parameters of the power Rayleigh (PR) distribution under a unified hybrid censoring scheme (UHCS). The research employs both Bayesian and Frequentist approaches, utilizing maximum likelihood estimation (MLE) alongside Bayesian estimates derived through Markov Chain Monte Carlo (MCMC) methods. The study incorporates symmetric and asymmetric loss functions, specifically general entropy (GE), linear expoential (LINEX), and squared error (SE), to evaluate the performance of the estimators. A Monte Carlo simulation study is conducted to assess the effectiveness of the proposed methods, revealing that Bayesian estimators generally outperform Frequentist estimators in terms of mean squared error (MSE). Additionally, the paper includes a real-world application involving ball bearing lifetimes, demonstrating the practical utility of the proposed estimation techniques. The findings indicate that both point and interval estimates exhibit strong properties for parameter estimation, with Bayesian estimates being particularly favored for their accuracy and reliability.