Inference on Reliability Characteristics of the Bounded Weighted Exponential Distribution Under Modified Multiple-Interval Type-I Censoring: A Classical and Bayesian Approach

This paper investigates statistical inference for the bounded weighted exponential BWE distribution using lifetime data obtained under a modified multiple-interval type-I censoring scheme (MMITICS). Within this framework, we develop methods based on maximum likelihood estimation, maximum product spacing estimation, and Bayesian inference to estimate the model parameters as well as the associated reliability measures. In addition, bootstrap confidence intervals using both likelihood-based and product-spacing-based formulations are obtained. For the Bayesian analysis, posterior estimates are derived using both likelihood-based and product-spacing-based formulations. Asymptotic confidence intervals are constructed using frequentist procedures, while Bayesian highest posterior density credible intervals are obtained through a Markov Chain Monte Carlo algorithm employing Gibbs sampling combined with Metropolis-Hastings steps for posterior computation. An extensive Monte Carlo simulation study is carried out to evaluate and compare the statistical performance of the proposed estimators. Furthermore, the optimal design of the MMITICS is investigated using both classical and Bayesian optimality criteria. Finally, two real data sets are analyzed to illustrate the practical applicability and robustness of the proposed methods.