統計檢定法應用於區域頻率分析之研究

Statistical Tests Applied for Regional Frequency Analysis

張斐章(FI-JOHN CHANG) ； 吳正吉(CHENG-CHI WU) ； 王文清(WEN-CHANG WANG)

《台灣水利》 45卷4期 (1997/12) Pp. 45-55+23

摘要

進行區域頻率分析時，通常利用適合度檢定與均勻性檢定以確定區域的機率分佈型態與均勻程度。惟不同檢定法之檢定結果並不盡相同，本研究以蒙地卡羅法（Monte Carlo），比較平均相對誤差法（ARE）、平均標準差法（ASE）二者鑑別率的優劣，結果顯示ARE法在大部份的情況下，其鑑別率皆高於ASE法；尤其在小樣本（記錄年限較短）時，ARE法的鑑別率隨區域測站數的增加，成長的幅度較大。再則，於各機率分佈之鑑別率差異性比較，在小樣本時ARE法的差異較不明顯；此現象表示，在小樣本時ARE法誤判的機率小於ASE法。本研究以台灣南部地區為研究範例，進行年最大一日暴雨之區域頻率分析。首先利用多變量的方法－主成份分析（Principal Component Analysis）與群集分析（Cluster Analysis），歸類分群具有相同機率分佈之降雨區域。再針對分群的結果分別進行區域適合度檢定與均勻性檢定。結果顯示：第A群和第B群具有PT3機率分佈的特性；第C群和第D群具有GEV機率分佈的特性。

關鍵字

區域頻率分析 ； 適合度檢定 ； 均勻性檢定 ； 平均標準差法 ； 平均相對誤差法

並列摘要

In regional frequency analysis, the goodness-of-fit test and the homogeneity test are usually used to identify the probability distribution and homogeneity degree of the region, but the different methods are not always with the same results. The Monte Carlo method has been performed to compare the distinguishing ability for the criteria of Average Relative Error (ARE) and Average Standard Error (ASE), and the results show that in most of the cases the ARE is better than the ASE. The growing rate of distinguishing ability of ARE is larger than ASE when the region's sets is increased, especially when the data number is small. Comparing the distinguishing ability in probability distribution, the differences among these probability distributions for ARE are not so apparent in small sample size. It means that the misjudgment of ARE is less than ASE in small sample size. The research make an example of regional frequency analysis for annual maximum daily rainfall in southern Taiwan. The multivariate statistical methods-principal component analysis and cluster analysis have been used, in the beginning, to identify the rainfall areas with the same population distribution. The classified regions are then examined by the goodness-of-fit test and the homogeneity test. As a result, the A and B regions own the character of PT3 distribution, while the C and D. regions have the character of GEV distribution.

並列關鍵字

Regional frequency analysis ； goodness-of-fit test ； Homogeneity test ； Average Relative Error ； Average Standard Error