In this study, the estimation of the parameters of the two parameters exponential distribution based on progressive Type II censored data is considered. Assuming both location and scale parameters to be unknown, the maximum likelihood(ML), penalized maximum likelihood (PML) and Bayes estimators are obtained. The results indicate that the PMLE is the same as the uniformly minimum variance unbiased estimator (UMVUE). Further, the mean square errors of proposed estimators both analytical and Monte Carlo simulation study for different types of censoring schemes are computed. The results reveal that the PMLE and Bayes estimators outperform the MLE ones. This paper comes to an end by presenting an illustrative example.
