Reliability Estimation for the Inverse Weibull Distribution Under Adaptive Type-II Progressive Hybrid Censoring: Comparative Study - Alslman, Majd; Helu, Amal (Statistics, Optimization & Information Computing, 2023)
The aim of this study is to investigate different methods of estimating the stress-strength reliability parameter, θ =P(Y<X), when the strength (X) and the stress (Y) are independent random variables taken from the inverse Weibull distribution (IWD), with the same shape parameter and different scale parameters. Based on Adaptive Type-II Hybrid progressive censored samples, we employ classical and Bayesian approaches. In the classical approach, we use the maximum likelihood estimator (MLE), the approximate maximum likelihood estimator (AMLE), and the least squares estimator (LSE). In contrast, the Bayesian approach utilizes symmetric and asymmetric loss functions. Due to the absence of explicit forms for Bayes estimators, we propose using Lindley’s approximation method for computing the Bayes estimators. We compare these estimators using extensive simulations and two criteria: the bias and the mean square error (MSE). Finally, two real-life data examples are provided for illustrations.