Asymptotic Prediction for Future Observations of a Random Sample of Unknown Continuous Distribution

When the first r lower extreme order statistics (failure times) of a sample large size id="M2">n, 1<r<s<n , are observed, asymptotic predictive intervals future statistic with rank id="M3">s constructed. The only assumption that we adopt is failure time attracted to Weibull distribution. In addition, suggest an efficient point estimator its shape parameter and then confidence interval constructed for it. Moreover, new interesting properties distributions belong minimum domain attraction distribution revealed. Furthermore, extensive simulation studies conducted demonstrate efficiency proposed methods. Two real datasets analyzed illustrate corroborate obtained results. main results concern samples.