Summary: This article deals with the problem of estimating exponential parameters, on the basis of a general progressive Type II censored sample, using both classical and Bayesian viewpoints. A class of natural prior densities is considered in the Bayesian setting. Even though maximum likelihood and highest posterior density estimators do not admit closed form expressions, explicit sharp lower and upper bounds are provided in this paper. These estimators are also found to have as good large-sample properties as those of the best linear unbiased estimator.
In the Bayesian framework, posterior density and distribution functions are derived explicitly. Assuming squared error-loss functions, Bayes estimators are obtained in closed forms. Credibility intervals and Bayes estimators under linear loss functions can readily be computed iteratively. Finally, an illustrative example is also included.