Bayesian parameter estimation and failure time prediction under double Type-II hybrid censoring for the generalized inverse exponential distribution - Shi Wei; Guoyuan He; Dalong Mo (Alexandria Engineering Journal)
This study examines parameter estimation and failure time prediction for products following the Generalized Inverse Exponential Distribution (GIED) under double Type-II hybrid censored data. We derive maximum likelihood estimates for parameters and compute Bayesian estimates and E-Bayesian estimates under four loss functions (symmetric and asymmetric). The asymptotic properties of these estimators are established. For failure time prediction, conditional median and Bayesian methods are used to generate point and interval predictions. Monte Carlo simulations compare the performance of maximum likelihood estimates, Bayesian estimates, and E-Bayesian estimates, benchmarked against least squares estimation. Results show that E-Bayesian estimates outperform Bayesian methods by reducing hyperparameter sensitivity, especially in small samples. The framework remains robust under prior mis-specification or deviations from GIED assumptions. Two real-world datasets validate the accuracy of the proposed methods, with predicted failure times and intervals aligning closely with observations.