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.