| Abstract: | 本研究以合成資料探討當資料不滿足極端 值理論之兩項基本假設:(1)族群內資料須屬同 一機率分布且相互獨立,及(2)族群內資料樣本 數需趨近無限大,時對極端值I型分布之適用性 。研究中採用機率點繪相關係數檢定 ( Probability plot correlation coefficient test)法,藉其能 正確反映I型誤差(Type I error)之特性,由通過檢 定之組數是否合理,探討相關性資料於極端值I 型分布之適用性及其應用時之效力。 研究結果顯示,資料之相關性愈強,極端值I 型分布愈不適用;即使當族群內樣本數為365時, 亦不保證極端值I型分布適用,主要因受族群內 資料偏態係數影響。同時,當族群內資料之偏 態係數接近極端值I型分布理論偏態係數值1.139 時,不論相關性及族群內之樣本數大小,極端值I 型分布皆適用。另,機率點繪相關係數檢定法 應用於極端值I型分布時其效力遠較K.S.檢定為 佳。
The aptness of extreme value type I distribution for the data which do not satisfy the basic assumptions of extreme value theory is investigated by synthetic data in the present study. The basic assumptions are that (1) data within group obey the same probability density function and do not mutually depend each other, and (2) the sample size of each group should approaches infinite. The probability plot correlation coefficient test is employed in this study. This is done by judging whether the percentage of rejecting the null hypothesis is reasonable, since this test preserves the type I error. The results indicates that extreme value type I distribution is not appropriate when the data are highly correlated, and even when the sample size of each group is 365. The major influence factor is the skewness coefficient of data for each group. Meanwhile, no mater how strong the correlation is and how large the sample size of data within group is, extreme value type I distribution is always appropriate whenever the skewness coefficient of data within group is close to 1.139 which is the theoretical skewness coefficient of extreme type I distribution. Besides, the results indicates that the probability plot coefficient test is more powerful than K.S. test. |
