In this article, a new censoring scheme is considered, namely, a middle part of a random sample is censored. A treatment for reconstructing the missing ORDER STATISTICS is investigated. The proposed procedure is studied in detail under exponential distribution which is widely used as a constant failure model in reliability.Different approaches are used to obtain point and interval reconstructors and then they are compared. A numerical example is presented for illustrating all the proposed inferential procedures. Eventually, we present some remarks including how the results of the paper can be used when the parameters of the exponential distribution are unknown.

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In this paper‎, ‎ORDER STATISTICS and associated inferences are considered from Lindley distribution‎. ‎We derive the exact forms of means‎, ‎variances and covariances as well as the moment generating functions of ORDER STATISTICS‎. ‎These obtained forms allow us to compute the means‎, ‎variances‎, ‎and covariances of the ORDER STATISTICS for various values of the shape parameter‎. ‎These values are then used to compute the coefficients of the best linear unbiased estimators‎, ‎the best linear invariant estimators‎, ‎and the least square estimators of the location and scale parameters‎. ‎The variances and covariances of these estimators are also presented‎. ‎Using the best linear unbiased estimators and best linear invariant estimators we construct confidence intervals for the location and scale parameters through Monte Carlo simulations‎. ‎In addition‎, ‎based on the ORDERed data‎, ‎we investigate how to obtain the best linear unbiased predictor and the best linear invariant predictor for future ORDER STATISTICS‎. ‎Finally‎, ‎data analysis and Monte Carlo simulation have been performed for illustrative purposes and comparative studies‎, ‎respectively.