Optimal Prediction of Future Order Statistics Using Conditional Expectation under Type II Censoring for Continuous Distributions

Abstract

This study introduces a novel methodology for predicting future order statistics under Type II censoring, using conditional expectation to derive optimal predictors with minimal mean squared error (MSE). Two distinct predictors are proposed: one based on properties of exponential spacings  and another utilizing uniform order statistics. The theoretical framework is validated through extensive simulations across various distributions (Weibull, Pareto, Gamma, Beta, and Normal), demonstrating superior accuracy compared to existing methods. The exponential-based predictor excels in heavy-tailed scenarios, while the uniform-based predictor offers computational efficiency for light-tailed  scenarios or symmetric distributions. Additionally, the paper provides techniques for constructing confidence intervals for future order statistics and applies the methodology to real-world data, showcasing its practical utility in reliability engineering and survival analysis.