Comparison of Estimates and Predictors using Joint Type-II Progressive Censored Samples from two Generalized Rayleigh Distribution

Recently, the progressive Type-II censoring has been extended to conduct comparative life-testing experiment of different competing products, which tackles the lifetimes of two samples simultaneously. Here we consider the problem of the joint progressive censoring data coming from the two generalized Rayleigh distributions. The estimation of the unknown parameters and prediction of the life times of the censored units of the joint progressively censored sample are discussed. Frequentist and Bayesian analyses are adopted for conducting the estimation and prediction problems. The likelihood method, bootstrap methods as well as the Bayesian sampling techniques are applied for the inference problems. The point predictors and credible intervals of the times of future failure based on an informative observed censoring units can be developed. Monte Carlo simulations are performed to compare the so developed methods and one real data set is analyzed for illustrative purposes.