Bayesian and Classical Inference for the Weighted Exponential‐Lindley Distribution Under Adaptive Type‐ II Hybrid Progressive Censoring

Abstract

Censoring strategies in reliability testing are often adopted to control testing time, sample size, and cost. To improve inferential efficiency under such settings, this study considers an adaptive Type‐II hybrid progressive censoring scheme. The recently proposed one‐parameter Weighted Exponential–Lindley distribution is considered for modeling censored lifetime data. Both classical and Bayesian estimation approaches are developed for the model parameters, as well as for reliability and hazard rate functions. The classical inference is carried out using the maximum likelihood estimation, and approximate confidence intervals are constructed for the unknown parameter and reliability characteristics. Bayesian estimation is performed assuming a gamma prior under symmetric and asymmetric loss functions. Since the joint posterior distribution is analytically intractable, the Markov chain Monte Carlo technique is employed to obtain Bayes estimates and construct the highest posterior density credible intervals. The performance of the proposed estimators is examined through extensive simulation studies under different progressive censoring schemes. A real data application demonstrates the practical relevance and effectiveness of the proposed model.