observed under type-II censoring. We obtain maximum likelihood estimates and associated interval estimates under a classical approach, and Bayes estimates using various loss functions and associated highest posterior density interval estimates. Maximum likelihood estimates are obtained using the Newton-Raphson method and Expectation Maximization (EM) algorithm, and Bayes estimates are computed using importance sampling and Lindley approximation. We also compute shrinkage preliminary test estimates based on maximum likelihood and Bayes estimates. Further, we provide inference on the censored observations by making use of best unbiased and condition median predictors under a classical approach, and predictive estimates under the Bayesian paradigm using importance sampling. The associated predictive interval estimates are also obtained using different methods. Finally, we conduct a simulation study to compare the performance of all the proposed methods of estimation and prediction, and analyze a real data set for illustration purpose.

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In this paper we address the problems of estimation and prediction when lifetime data following Burr type III distribution are observed under progressive type-I hybrid censoring. We first obtain maximum likelihood estimators of unknown parameters using expectation maximization and stochastic expectation maximization algorithms, and associated interval estimates using Fisher information matrix. We then obtain Bayes estimators based on non-informative and informative priors under squared error, entropy and Linex loss functions using the method of Tierney-Kadane and importance sampling technique, and associated highest posterior density interval estimates by making use of Chen and Shao method. We further predict the censored observations and interval estimates under classical and Bayesian approaches. Finally we analyze two real data sets, and conduct a simulation study to compare the performance of various proposed estimators and predictors.

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