博碩士論文 103225007 詳細資訊




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姓名 吳偉豪(Wei-Hao Wu)  查詢紙本館藏   畢業系所 統計研究所
論文名稱 有母數的強韌適合度檢定
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摘要(中) 我們使用伽瑪分配做為模型的假設,利用此分配能夠在分配假設不正確的情況之下,仍然能夠正確的估計母體平均數的特點,來製造新的適合度檢定統計量來檢定資料是否來自某一個特定的分配。本文將選用Kolmogorov-Smirnov (Kolmogorov,1933;Smirnov,1939)、Cramér–von Mises(Cramér,1928;von Mises,1931)與Anderson-Darling(1952)三個檢定統計量作比較。
摘要(英) We take advantage of the property that the gamma distribution is able to deliver consistent estimate for the mean parameter under model misspecification to develop a goodness of fit (GOF) test statistic. We use simulations to compare our novel test statistic with other GOF methods including the Kolmogorov-Smirnov、Cramér–von Mises and Anderson-Darling tests. It appears that our test outperforms in terms of testing power when the underlying distributions are similar to the null hypothesized distribution.
關鍵字(中) ★ 適合度檢定
★ 經驗分配
★ 強韌
★ 伽瑪分配
★ 韋伯分配
★ 對數常態分配
★ Burr分配
關鍵字(英) ★ Goodness of Fit
★ Empirical distribution
★ robust
★ gamma distribution
★ Weibull distribution
★ lognormal distribution
★ Burr distribution
論文目次 摘要 .........................................................................................................................i
Abstract ........................................................................................................................ii
致謝 .......................................................................................................................iii
目錄 .......................................................................................................................iv
表目錄 .......................................................................................................................vi
第一章 緒論 ........................................................................................................1
第二章 分配介紹 ................................................................................................3
2.1 伽瑪分配 ........................................................................................3
2.2 韋伯分配 ........................................................................................4
2.3 對數常態分配 ................................................................................5
2.4 Burr分配 ........................................................................................5
第三章 使用經驗分配函數的適合度檢定 ........................................................8
3.1 三種經驗分配檢定統計量 ................................................................8
3.2 經驗分配適合度檢定的執行步驟 ..............................................10
第四章 根據強韌性質的適合度檢定 ..............................................................11
4.1 強韌的適合度檢定統計量 ..............................................................11
4.2 變異數 的估計 ..............................................................................12
第五章 模擬研究 ..............................................................................................14
5.1 :資料來自對數常態分配的假設 ..............................................14
5.2 :資料來自韋伯分配的假設 ..............................................15
第六章 實例分析 ..............................................................................................32
6.1 實例1 ..............................................................................................32
6.2 實例2 ..............................................................................................33
6.3 實例3 ..............................................................................................34
第七章 結論 ......................................................................................................36
參考文獻 ......................................................................................................37
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2. Cramér, H. (1928). "On the Composition of Elementary Errors". Scandinavian Actuarial Journal, 11, 13-74 and 141-180.
3. Kalbfleisch, J.D., Lawless, J.F. (1992). Some useful statistical methods for truncated data. Journal of Quality Technology, 24, 145-52.
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10. Nelson, W. B. and Doganaksoy, N. (1995) . Statistical nalysis of Life or Strength Data from Specimens of Various Sizes Using the Power–(log) Normal Model, In Recent Advances in Life-Testing and Reliability, N. Balakrishnan, Ed., pp. 377-408, CRC Press, Boca Raton.
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13. Robert N. Rodriguez. (1977). A Guide to the Burr Type XII Distributions. Biometrika, 64: 129-134.
14. Schafft, H.A., Staton, T.C., Mandel, J., and Shott, J.D. (1987). Reproducibility of Electromigration Measurements, IEEE Trans Electron Devices, ED-34, 673-681.
15. Stephens, M.A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons. Journal of the American Statistical Association, 69, 730-737
16. Tsou, T-S (2009). Performing Legitimate Parametric Regression Analysis without Knowing the True Underlying Random Mechanisms. Communications in Statistics-Theory and Methods, 38: 1680–1689.
17. van der Vaart, A. W. (2000). Asymptotic Statistics, Cambridge University Press, Cambridge.
18. von mises R. (1931). Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik,Leipzig und Wien.
19. Watson, G. S. (1961). Goodness of fit tests on the circle. Biometrika, 48:109-
114.
指導教授 鄒宗山(Tsung-Shan Tsou) 審核日期 2016-7-25
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