序率模擬應用於機率分佈適合度檢定之評估

Accuracy Assessment of Test of Goodness-of-fit by Stochastic Simulation

許介維(Chieh-Wei Hsu)

指導教授 ： 鄭克聲

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.01453

摘要

無資料

關鍵字

適合度檢定 ； 序率模擬 ； 檢定力 ； 型I錯誤

並列摘要

Chi-squared and Kolmogorov-Smirnov tests are two most widely applied methods for goodness-of-fit test. In application of these tests to hydrological frequency analysis, we often encounter the problem of having data with short record length or sample size. Sample size of a random sample affects the accuracies of parameters estimation and goodness-of-fit test. This study, through stochastic simulation of random variables of normal, log-normal, Extreme Value Type I (EV1), Pearson Type III (PT3) and log-Pearson Type III (LPT3) distributions, compares the performance of and K-S tests with respect to type-I-error and power.

When population parameters are known, test outperforms the K-S test with very small type-I-error even for sample size as small as 50. When the goodness-of-fit test is conducted with estimated parameters (the null distribution is specified using estimated parameters), it is found that skewness has significant effect on type-I-error of tests. Power of the test is also found to increase with level of significance, sample size and skewness.

Keywords: goodness-of-fit test, stochastic simulation, power, type-I-error

並列關鍵字

goodness-of-fit test ； stochastic simulation ； power ； type-I-error

參考文獻

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