Point prediction for the proportional hazards family based on progressive Type-II censoring with binomial removals

‎In this paper‎, ‎some different predictors are presented for failure times of units censored in a progressively censored sample from proportional hazard rate models‎, ‎where the number of units removed at each failure time follows a binomial distribution‎. ‎The maximum likelihood predictors‎, ‎best unbiased predictors and conditional median predictors are derived‎. ‎Also‎, ‎the Bayesian point predictors are investigated for the failure times of units with the three common loss function‎. ‎Finally‎, ‎a numerical example and a Monte Carlo simulation study are carried out to compare all the prediction‎ ‎methods discussed in this paper.