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Robust Procedures for Estimating the Scale Parameter and Predicting Future Order Statistics of the Weibull Distribution

Two robust estimators of the scale parameter of the Weibull distribution are proposed: 1) Maximin Estimator (based on a mixture of Weibull distributions and the procedure of constructing the Best Linear Invariant Estimator), and 2) Adaptive Estimator (based on an adaptive procedure which chooses between the Maximin Estimator and the Best Linear Invariant Estimator from individual Weibull distributions). They are robust compared with some well-known estimators. Using similar methods, two robust predictors of future order statistics in a sample are proposed: 1) Maximin Predictor, and 2) Adaptive Predictor. The ideas behind the construction of the estimators and predictors can be applied to other distributions.