Estimation and prediction for two-parameter Pareto distribution based on progressively double Type-II hybrid censored data

In this paper, a new censoring test plan called progressively double Type-II hybrid censoring scheme is introduced for the first time. Based on this type of censored data, the maximum likelihood estimates of the unknown parameters and reliability for the two-parameter Pareto distribution are obtained. Using the Bayesian method, the Bayesian estimates of the unknown parameters and reliability are obtained under the symmetric and asymmetric loss functions. The failure times of all withdrawn units are predicted using the classical and Bayesian methods, including the predictive values and the prediction intervals. The mean values and mean square errors of the estimators are calculated by Monte-Carlo simulation, and the mean square errors between them are compared, and the results show that all Bayesian estimates are better than the corresponding maximum likelihood estimates. Using a real data set, we compute the Bayesian estimates of the unknown parameters and reliability, and predict the observations of the censored units.