序率模擬應用於水文分布檢定信賴區間之建立

Establishing Confidence Interval for Goodness-of-Fit Test by Stochastic Simulation

鄭克聲(Ke-Sheng Cheng) ； 吳宜珍(Yii-Chen Wu)

《農業工程學報》 52卷4期 (2006/12) Pp. 71-79

摘要

水文頻率分析在傳統上主要利用χ^2檢定與K-S檢定決定選用之機率分布，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。故本文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。研究中，以常態分布做為方法的介紹，並由於在參數推估方面，線性動差法的推估量較動差法有較小的偏估，所以本研究加入線性動差比圖，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。

關鍵字

序率模擬 ； 適合度檢定 ； 信賴區間 ； 動差法 ； 線性動差法

並列摘要

Rainfall frequency analysis is a prerequisite for many hydrological engineering projects. It yields an amount which corresponds to a pre-specified probability of exceedance, also know as the design rainfall, for the interested hydrological variable. The accuracy of frequency analysis will inevitably affect the safety level and cost of the engineering projects. Frequency analysis involves choosing the types of probability distributions which characterize the statistical properties of the hydrological variables and estimating distribution parameters for the chosen distribution. However, uncertainties are always embedded in choosing the distribution type and parameters estimation. Therefore, it is imperative to investigate how the most adequate type of distribution can be determined by considering the uncertainties.
In this study, we focus on the effect of sample size on the confidence intervals of hypothesis test for normal distribution. The empirical joint probability distribution of the 3(superscript rd) and 4(superscript th) product-moment-ration (PMR) and linear-moment-ration (LMR), with respect to various sample sizes, were constructed by stochastic simulation. Then an algorithm was developed to delineate the sample-size-dependent 95% confidence regions of the PMR and LMR diagrams. Finally, the established confidence regions were verified by stochastic simulation. The results demonstrate that the established confidence intervals can be used for goodness-of-fit tests and, in particular, the critical intervals of PMR diagram have ellipse shapes and can be easily fit to mathematical models.

並列關鍵字

Stochastic simulation ； Goodness-of-fit test ； Confidence interval ； Moment method ； L-moment method