Inference and optimal design for doubly censored data using generalized lifetime distribution family

In this paper, we address the challenging problem of statistical inference for unknown parameters in generalized lifetime distributions under double censoring. We propose classical and Bayesian estimation approaches for these parameters, incorporating a range of loss functions in the Bayesian framework to improve flexibility and estimate accuracy. The Bayesian inference is implemented using the Metropolis-Hastings algorithm within a Markov Chain Monte Carlo setting to generate posterior samples. These samples are subsequently utilized to compute Bayes estimates and construct credible intervals, thereby providing a comprehensive measure of parameter uncertainty. The performance of the proposed methods is systematically evaluated through simulation studies, which assess their accuracy under various censoring schemes. Additionally, we present two real-data examples to illustrate the practical applicability and utility of the methods in addressing doubly censored data. Furthermore, we explore optimal experimental design considerations, proposing experimental plans specifically tailored to the double-censoring structure. This study offers new insights into the design and analysis of experiments where double censoring is prevalent, with the potential to optimize both time and resource allocation in such studies.