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極端值I型分布於相關性水文資料適用性之研究
Study on the Aptness of Extreme Value Type I Distribution for Correlated Hydrological Data
摘要
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）族羣內資料須屬同一機率分布且相互獨立，及（2）族羣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。最後，藉機率點繪相關係數檢定探討極端值I型分布於本省年一、二及三日最大暴雨之適用性。研究結果顯示，資料之相關性愈强，極端值I型分布愈不適用；卽使當族羣內樣本數爲365時，亦不保證極端值I型分布適用，主要因受族羣內資料偏態係數影響。同時，當族羣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，不論相關性及族羣內之樣本數大小，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。於實測資料方面，就整體而言，極端值I型分布並不適用本省年一、二及三日最大暴雨。
並列摘要
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 approach 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 indicate 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 influenct factor is the skewness coefficient of data for each group. Meanwhile, no matter 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 indicate that the probability plot coefficient test is more powerful than K. S. test. In general, extreme value type I distribution is not appropriate for the annual maximum 1-day, 2-day and 3-day precipitation.