Prediction of future events on the basis of the past and present information is a fundamental problem of statistics, arising in many contexts and producing varied solutions. The predictor can be either a point or an interval predictor. This paper focuses on predicting the future observations from the modified Topp-Leone Chen distribution based on progressive Type-II censored scheme. The two-sample prediction is applied to obtain the maximum likelihood, Bayesian and E-Bayesian prediction (point and interval) for future order statistics. The Bayesian and E-Bayesian predictors are considered based on two different loss functions, the balanced squared error loss function; as a symmetric loss function and balanced linear exponential loss function; as an asymmetric loss function. The predictors are obtained based on conjugate gamma prior and uniform hyperprior distributions. A numerical example is provided to illustrate the theoretical results and an application using real data sets are used to demonstrate how the results can be used in practice.

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Lifetime distributions under progressive Type-II censored scheme have been attracting great interest due to their wide application in the fields of science, engineering, social sciences and medicine. Also, prediction of future events on the basis of the past and present knowledge without any doubt is one of the most important problems in statistics. In this paper, the Bayes estimators for the parameters of the Marshall-Olkin Weibull-exponential distribution are derived based on progressive Type-II censored scheme. The estimators are considered under two different loss functions, the balanced squared error loss function; as a symmetric loss function and the balanced linear exponential loss function; as an asymmetric loss function. Also, the two-sample prediction method is applied to obtain the Bayesian prediction (point and interval) for future order statistics. A numerical example is provided to illustrate the theoretical results and an application using real data set is used to demonstrate how the results can be used in practice.