線性動差比適合度檢定之檢定力測試

Assessing Power of Test for Goodness-of-Fit Test Using L-Moment-Ratios Diagram

劉俊志(Jun-Jih Liou) ； 吳宜珍(Yii-Chen Wu) ； 江介倫(Jie-Lun Chiang) ； 鄭克聲(Ke-Sheng Cheng)

《農業工程學報》 53卷4期 (2007/12) Pp. 80-91

https://doi.org/10.29974/JTAE.200712.0007

摘要

水文頻率分析爲水利工程設計的重要依據。傳統上利用卡方(χ^2)檢定和科司(Kolmogorov-Smirnov)檢定等適合度檢定法來決定水文頻率分析之最適機率分佈。近年來所發展之線性動差法，於母體參數之推估表現上，幾近不偏推估，同時，不同機率分佈之出象樣本散佈圖，呈現高分辨率之特質，因此圖內外學者廣泛使用線性動差比圖，作爲選定水文機率分佈之依據。
本研究使用序率模擬法，進行線性動差比值適合度檢定、卡方檢定與科司檢定之檢定力比較。結果顯示，線性動差比值適合度檢定之檢定力明顯優於傳統之適合度檢定方法。

關鍵字

頻率分析 ； 適合度檢定 ； 卡方檢定 ； 科司檢定 ； 線性動差法

並列摘要

Hydrological frequency analysis is one of the essential tasks in hydrological engineering design. Conventional methods of goodness-of-fit test, including χ^2 test and Kolmogorov-Smirnov (KS) test, are used to determine the best-fit probability distribution for hydrological data. Recently, L-moment method is widely used in frequency analysis in that it is almost unbiased in parametric estimation, and L-moment-ratios diagrams have been suggested as a useful tool for selecting a best-Fit distribution among candidate ones.
Using stochastic simulation, recent studies had established a new method for goodness-of-fit test by acceptance regions of several distributions, including. Normal Extreme Value Ⅰ, and Pearson Type Ⅲ distribution, on L-moment diagram. However, only few studies have so far been made at comparisons of power of tests among the new method and conventional ones. Therefore, the purpose of power of tests among the new method and conventional ones. Therefore, the purpose of this study is to compare the power of test of several goodness-of-fit tests, including χ^2 test, KS test, and a new method based on L-moment diagram. It is found that new L-moment-ratios based test is superior to other conventional ones.

並列關鍵字

Frequency analysis ； Goodness-of-fit test ； χ^2 test ； KS test ； L-moment method