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中文論文名稱 多種檢定均勻性方法的檢定力研究
英文論文名稱 A variety of test methods for testing homogeneity forces
校院名稱 淡江大學
系所名稱(中) 中等學校教師在職進修數學教學碩士學位班
系所名稱(英) Executive Master's Program In Mathematics for Teachers
學年度 101
學期 2
出版年 102
研究生中文姓名 陳瑩曦
研究生英文姓名 Ying-Hsi Chen
學號 700190092
學位類別 碩士
語文別 中文
口試日期 2013-06-30
論文頁數 29頁
口試委員 指導教授-伍志祥
委員-張三奇
委員-楊恭漢
中文關鍵字 卡方適合度檢定  頻率移動平均卡方檢定  Greenwood檢定 
英文關鍵字 chi-square goodness-of-fit test statistics  moving average frequency chi-square statistics  Greenwood test 
學科別分類
中文摘要 在眾多適合度檢定的方法中,最常被提及的皮爾遜卡方檢定(Pearson chi-square test)會因為分割起始點(cell point)的選取,造成檢定結果的差異。起始點的選取,可以等價於用0當起始點但使用轉換的資料來做卡方檢定。資料轉換對其他的檢定方法的檢定力影響,是沒被討論的議題,本論文以模擬研究來討論常見的檢定方法的檢定力會如何受影響。
另外本研究還提出皮爾遜卡方檢定的裁剪統計量,我們把區間[0,1]等分割,使其分割格子數與樣本數一樣多,再計算對每一個格子擁有的樣本頻率值的移動平均值,用這些頻率移動平均值來做卡方檢定。從模擬研究中可以發現其檢定力比較穩定,不太會受資料轉換的影響。若與高階間距為基礎所建立的檢定來比較兩者的檢定力,可以發現各有擅長。不似傳統卡方檢定其相對於以間距為基礎所建立的檢定方法,有明顯且有較差的表現。
英文摘要 Among the many methods of goodness-of-fit test, the most frequently mentioned is the traditional Pearson chi-square statistics. But chi-square test because of segmentation starting(cell point) the selection , resulting in differences in test results. Select a starting point(cell point), you can use 0 as the starting point is equivalent to using the conversion of data to do chi-square test. Data Conversion to other test methods impact test force is not being discussed topics of this thesis to discuss common analog test methods test force might be impacted
In addition the study also suggested crop Pearson chi-square test statistic, we interval [0,1] so divided so lattice division number of samples as many, and then calculate for the lattice for each sample has a moving average frequency value, moving average of these frequencies to do with chi-square test. Can be found from the simulation study of its test force is relatively stable and less affected by the impact of data conversion. If the spacing is based on the established order of the test to compare the test force can be found their own good. Unlike conventional chi-square test with respect to space-based verification method established, there are clear and there is poor performance.
論文目次 目 錄
第一章 緒論 …………………………………………… 1
第二章 頻率移動平均卡方檢定統計量(FMACS) …… 5
第三章 變換點的影響及檢定力的比較……………… 9
第一節 變換點的影響 …………………………… 9
第二節 檢定力的比較 ………………………… 14
第四章 結論…………………………………………… 22
參考文獻 …………………………………………. 23
附錄一 …………………………………………… 24
附錄二 ………………………………………… 26
附錄三 …………………………………………… 28

表 目 錄
表3-2-1 FMACS檢定與 TUOS及Gr檢定在 下的Power比較……15
表3-2-2 FMACS檢定與 TUOS及Gr檢定在 下的Power比較……17
表3-2-3 FMACS檢定與 TUOS及Gr檢定在 下的Power比較 … 19












圖 目 錄
圖3.1.1 分布F(x) 變換點與檢定力的關係圖………………………10
圖3.1.2 beta分布 變換點與檢定力的關係圖………………………11
圖3.1.3分布F(x) 變換點與檢定力的關係圖………………………11
圖3.1.4 beta分布 變換點與檢定力的關係圖………………………12
圖3.1.5 分布F(x) 變換點與檢定力的關係圖………………………12
圖3.1.6 beta分布 變換點與檢定力的關係圖………………………13


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Giornale dell’Istituta Italiano degli Attuari,1933, 4, 83–91.
Cressie, N. An Optimal Statistic Based on Higher Order Gaps. Biometrika, 1979,
66, 619–628
C.G. McLaren and M.A. Stephens. Percentage points and power for spacings
statistics for testing uniformity. Technical Report, Department of Mathematics and Statistics, Simon Fraser University. 1985.
Darling, D.A. The Kolmogorov-Smirnov, Cramer-von Mises Tests. Ann. Math. Statist.,1957, 28, 823–838
Dudewicz, E.J.; van der Meulen, E.C. Entropy-Based Tests of Uniformity. J. Amer.
Statist. Assoc., 1981, 76, 967–974.
Greenwood, M. The Statistical Study of Infectious Diseases. J. Roy .Statist. Soc. A,
1946, 109, 85–110
G.S. Watson. Goodness–of–fit on a circle. Biometrika, 1961, 48, 109–114.
Jammalamadaka, S. R., & Tiwari, R. C. Asymptotic comparison of three tests for
goodness of fit. Journal of Statistical Planning and Inference, 1985 ,2, 295-304.
Marsaglia, G. Monkeying with the goodness-of-fit test. Journal of Statistical Software, 2005,14(13), 1-4.
Misra, N., & van der Meulen, E. C. A new test of uniformity based on overlapping
sample spacings. Communications in Statistics-Theory and Methods, 2001, 30(7), 1435-1470.
N.H. Kuiper. Tests concerning random points on a circle. Proc. Koninkl.
Neder. Akad. van. Wetenschappen Series A, 1960, 63, 38–47.
Stephens, M.A. EDF Statistics for Goodness of Fit and Some Comparisons. J. Amer . Statist. Assoc., 1974, 69, 730–737.
T.W. Anderson and D.A. Darling (1954). A test of goodness–of–fit. Journal of the
American Statistical Association, 49, 765–769.
Wu, J.-S., & Deng-, W. Averaged shifted Chi-square Test. Journal of Nonparametric Statistics, 2011, 1-19.
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