On the Prediction of Future Order Statistics in the Weibull Distribution Using the Probability Charts

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  • 確率紙を利用したワイブル分布における未来標本の予測について
  • カクリツシ オ リヨウシタ ワイブル ブンプ ニ オケル ミライ ヒョウホン

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Abstract

This paper gives some results of study of predicting the future order statistics from the two-parameter Weibull distribition. Especially, whether the probability charts are usefull is examined. The prediction problem of the log-Weiblull variables which distribute as the extreme value variables are mainly discussed. Several methods using the probability charts are examined. The MSE's of the predictors obtained are compared with the well-known predictor BLIP and BLUP. They are exponentially transformed in order to obtain the predictors in the Weibull distribution. Then, the MSE's of these predictors are obtained by the computer simulation, and are mutually compared. As an important result, it is pointed out that the values of the moments of the order statistics are not necessary when the probability charts are used, and as far as we examine in this paper, fairly good predictors are obtained. Furtheremore it is pointed out that the extended Blom's estimation method is very usefull and simple.

This paper gives some results of study of predicting the future order statistics from the two-parameter Weibull distribition. Especially, whether the probability charts are usefull is examined. The prediction problem of the log-Weiblull variables which distribute as the extreme value variables are mainly discussed. Several methods using the probability charts are examined. The MSE's of the predictors obtained are compared with the well-known predictor BLIP and BLUP. They are exponentially transformed in order to obtain the predictors in the Weibull distribution. Then, the MSE's of these predictors are obtained by the computer simulation, and are mutually compared. As an important result, it is pointed out that the values of the moments of the order statistics are not necessary when the probability charts are used, and as far as we examine in this paper, fairly good predictors are obtained. Furtheremore it is pointed out that the extended Blom's estimation method is very usefull and simple.

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