In this study, the estimation of the two parameters exponential distribution based on progressive type II censored data were considered. The maximum likelihood(ML), penalized maximum likelihood (PML) and Bayes estimators assuming both of the location and scale parameters to be unknown were obtained. The results show that the PMLE is the same as uniformly minimum variance unbiased estimator (UMVUE). The mean square errors of proposed estimators both analytical and a Mont Carlo simulation study for different types of censoring schemes were computed. The simulation results revealed that the Bayes estimators outperforms the PMLEs. Further the PMLEs is superior to the MLEs.
