Classical and Bayesian Inference for the Two-Parameter Chen Distribution with Random Censored Data

This study explores classical and Bayesian estimation for the two-parameter Chen distribution with randomly censored data, where censoring times follow an independent two-parameter Chen distribution with separate shape and scale parameters. We first derive the maximum likelihood estimators of the unknown parameters, together with their asymptotic variances and credible intervals, and further adopt the method of moments, L-moments and least squares methods for classical estimation. Under the generalized entropy loss function and inverse gamma priors, Bayesian estimation is implemented via Gibbs sampling, with the highest posterior density credible intervals of parameters constructed accordingly. We also investigate the estimation of key reliability and lifetime characteristics of the distribution, and conduct Monte Carlo simulations to compare the performance of all aforementioned estimation methods. Finally, two real-world CMAPSS jet engine lifetime datasets from NASA are applied to validate the practical effectiveness of the proposed estimation approaches, demonstrating the enhanced flexibility of the Chen distribution compared to the exponential distribution in fitting aerospace-related censored data, given the marginal p-values in the K-S tests.