序率模擬應用於水文分佈檢定信賴區間之建立

Abstract

水文頻率分析為水利工程設計的重要項目之一，工程安全與否與頻率分析的結果有著莫大的關係存在。傳統上主要利用χ2檢定與K-S檢定來決定選用之機率分布，但在應用上，常遇到檢定資料為小樣本且具高偏態，此時檢定之準確性有待評估。在機率分布套配時，除了上述的兩種方法外，還可利用由三階動差與四階動差所構成的動差比圖，利用不同機率分布其具有不同形態的動差比圖，來區別檢定資料的機率分布。因此，本研究擬建立與樣本大小有關之機率分布檢定的信賴區間，以提供在選用機率分布時，可以透過此建立的95％信賴區間，決定適合的機率分布。研究中，以常態分布做為方法的介紹。 在參數推估方面，由於線性動差法的推估量較動差法有較小的偏估，所以本研究亦加入線性動差比圖，使得在決定機率分布時，不論使用動差法或線性動差法均有其動差比圖可以判別機率分布。 研究結果顯示，本研究中由偏態係數與峰度係數產生器、網格法建立樣本組體圖、樣本信賴區間演算及曲線套配等程序，所建立動差比圖的95%信賴區間，其形狀相似於前人研究。在信賴區間的驗証結果顯示，動差法和線性動差法所得到的信賴水準皆接近95％，所以此建立信賴區間的方法確實可行。

Hydrological frequency analysis is one of important things for hydrological engineering design. The result of frequency analysis will affect the safety of constructions. We mainly use χ2 test or K-S test to decide probability distribution in tradition. But our sample data is usually in small size and high skewness, so we need to evaluate the power of test. When fitting probability distributions, we also can use moment ratio diagram which is constructed by third moment and fourth moment. Different probability distributions have its specific type of moment ratio diagram, so we can use this characteristic to recognize probability distribution of sample data. In this study, the confidence intervals of different sample sizes of normal probability distribution will be established. It can be used to decide sample probability distribution. From the reason of L-moment method has smaller bias than moment method in parameters estimation, we also try to use it to make L-moment ratio diagram for probability distribution recognition. The results of this research indicate that the shape of confidence interval established for Goodness-of-Fit test is similar to fore studies. In the test result of confidence interval, the accuracy of moment and L-moment methods approximate to 95%, so the process of establishing confidence intervals for Goodness-of-Fit test is indeed feasible.