Advances in Bayesian and Non-Bayesian Approaches Under Progressive Type-II Censoring with Applications

Recent advances in lifetime modeling have led to several extensions of classical distributions, among which the extended inverted Kumaraswamy lifetime model, known as the exponentiated generalized inverted Kumaraswamy model, represents a significant innovation. In parallel, progressive Type-II censoring frameworks have garnered growing attention for their adaptability and relevance across various applied disciplines, including medical, engineering, and social sciences. Driven by this motivation, the present study focuses on the problem of parameter estimation for the proposed lifetime model under a progressive Type-II censoring scheme. Both Bayesian and non-Bayesian frameworks are utilized to estimate the model parameters, reliability function, and hazard rate. Furthermore, interval estimation is conducted by constructing confidence and Bayesian credible intervals for these measures. Assuming independent gamma priors, Bayes estimators are derived under both symmetric and asymmetric loss functions to account for different decision-making perspectives. In addition, conditional and Bayesian predictive analyses are developed within a two-sample prediction framework, and their associated prediction intervals are constructed. The efficiency and robustness of the proposed estimation and prediction methodologies are thoroughly evaluated through an extensive simulation study conducted under various sample sizes and censoring schemes. To further demonstrate the model’s practical relevance, real-world medical and engineering datasets are analyzed, highlighting the applicability and effectiveness of the proposed distribution in empirical contexts.