Frequentist and Bayesian Estimation Under Progressive Type-II Random Censoring for a Two-Parameter Exponential Distribution

In medical research, random censoring often occurs due to unforeseen subject withdrawals, whereas progressive censoring is intentionally applied to minimize time and resource requirements during experimentation. This work focuses on estimating the parameters of a two-parameter exponential distribution under a progressive Type-II random censoring scheme, which integrates both censoring strategies. The use of symmetric properties in failure and censoring time models, arising from a shared location parameter, facilitates a balanced and robust inferential framework. This symmetry ensures interpretational clarity and enhances the tractability of both frequentist and Bayesian methods. Maximum likelihood estimators (MLEs) are obtained, along with asymptotic confidence intervals. A Bayesian approach is also introduced, utilizing inverse gamma priors, and Gibbs sampling is implemented to derive Bayesian estimates. The effectiveness of the proposed methodologies was assessed through extensive Monte Carlo simulations and demonstrated using an actual dataset.