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題名 以經驗分佈函數為基準之適合度檢定方法
Alternative Goodness-of-Fit Tests based on Empirical Distribution作者 許晉瑋
Hsu, Chin-Wei貢獻者 洪英超
Hung, Ying-Chao
許晉瑋
Hsu, Chin-Wei關鍵詞 適合度檢定
經驗分佈函數
卡方適合度檢定
Anderson-Darling檢定
Kolmogorov-Smirnov檢定日期 2020 上傳時間 5-Feb-2020 17:06:58 (UTC+8) 摘要 適合度檢定為一種用以判斷某母體是否服從某特定分配的假設檢定，較為常用的一些適合度檢定有卡方適合度檢定，還有以經驗分佈函數（Empirical Distribution Function; EDF）為基準之適合度檢定，此類檢定的核心概念為評估經驗分佈函數與累積分佈函數（Cumulative Distribution Function; CDF）是否靠近，並以此建構合理的檢定統計量。此類檢定最為常用的為Anderson-Darling 檢定（A-D test）以及Kolmogorov-Smirnov 檢定（K-S test），A-D test 的檢定力普遍比K-S test 強，因其對分配的尾端較為敏感，但K-S test 執行起來較為簡單，亦可廣泛地延伸至多變量分配。本文主要是根據K-S test 的概念，定義一個稱為Lp-norm 的K-S 檢定統計量來執行連續型分配的適合度檢定。此方法可運用到單一變量及多變量分配的檢定，在電腦模擬的實驗下本文也證明所提方法於某些參數設定之下有較高的檢定力。 參考文獻 1. Alodat, M.T., Al-Subh, S.A., Ibrahim K., & Jemain A.A. (2010). “EmpiricalCharacteristic Function Approach to Goodness of Fit Tests for the LogisticDistribution under SRS and RSS”, Journal of Modern Applied Statistical Methods,Vol. 9, No. 2, 558-567.2. Bakshaev, A., & Rudzkis, R. (2015). “Multivariate goodness-of-fit tests based onkernel density estimators”, Nonlinear Analysis: Modelling and Control, Vol. 20, No.4, 585-602.3. Chen, W.C., Hung, Y.C., & Balakrishnan N. (2014) “Generating beta randomnumbers and Dirichlet random vectors in R: The package rBeta2009”,Computational Statistics and Data Analysis, 71, 1011-1020.4. Facchinetti, S. (2009) “A Procedure to Find Exact Critical Values of Kolmogorov-Smirnov test”, Statistica Applicata – Italian Journal of Applied Statistics, Vol. 21,No. 3-4, 337-359.5. Hung, Y.C., & Chen W.C. (2017). “Simulation of some multivariate distributionsrelated to Dirichlet distribution with application to Monte Carlo simulations”,Communication in Statistics-Simulation and Computation, Vol. 46, No. 6, 4281-4296.6. Justel, A., Pena, D., & Zamar, R. (1997). “A Multivariate Kolmogorov-SmirnovTest of Goodness of Fit”, Statistics and Probability Letters, 35, 251-259.7. McAssey, M.P. (2013) “An empirical goodness-of-fit test for multivariatedistributions’, Journal of Applied Statistics, 40:5, 1120-1131.8. Mirhossini, S.M., Amini M., & Dolati A. (2015) “On a general structure of bivariateFGM type distributions”, Application of Mathematics, Vol. 60, No. 1, 91-108.9. Razali , N.M., & Wah, Y.B. (2011) “Power comparisons of Shapiro-Wilk,Kolmogorov-Smirnov, Lillefors and Anderson-Darling tests”, Journal of StatisticalModeling and Analytics, Vol.2, No. 1, 21-33.10. R package “Emcdf” (2018). URL: https://cran.r-project.org/web/packages/Emcdf/index.html.11. R package “MultiRNG” (2019). URL: https://cran.r-project.org/web/packages/MultiRNG/index.html.12. R package “pbivnorm” (2015). URL: https://github.com/brentonk/pbivnorm.13. Stephens M.A. (1974). “EDF Statistics of Goodness of Fit and Some Comparisons”,Journal of the American Statistical Association, Vol. 69, No.347, 730-737.14. Vaidyanathan, V.S., & Varghese, S. (2016) “Morgenstern type bivariate Lindleydistribution”, Statistics, Optimization and Information Computing, Vol. 4, 132-146.15. Yang, G.Y. (2012). “The Energy Goodness-of-Fit Test for Univariate StableDistributions”. 描述 碩士
國立政治大學
統計學系
106354017資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106354017 資料類型 thesis dc.contributor.advisor 洪英超 zh_TW dc.contributor.advisor Hung, Ying-Chao en_US dc.contributor.author (Authors) 許晉瑋 zh_TW dc.contributor.author (Authors) Hsu, Chin-Wei en_US dc.creator (作者) 許晉瑋 zh_TW dc.creator (作者) Hsu, Chin-Wei en_US dc.date (日期) 2020 en_US dc.date.accessioned 5-Feb-2020 17:06:58 (UTC+8) - dc.date.available 5-Feb-2020 17:06:58 (UTC+8) - dc.date.issued (上傳時間) 5-Feb-2020 17:06:58 (UTC+8) - dc.identifier (Other Identifiers) G0106354017 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/128558 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 106354017 zh_TW dc.description.abstract (摘要) 適合度檢定為一種用以判斷某母體是否服從某特定分配的假設檢定，較為常用的一些適合度檢定有卡方適合度檢定，還有以經驗分佈函數（Empirical Distribution Function; EDF）為基準之適合度檢定，此類檢定的核心概念為評估經驗分佈函數與累積分佈函數（Cumulative Distribution Function; CDF）是否靠近，並以此建構合理的檢定統計量。此類檢定最為常用的為Anderson-Darling 檢定（A-D test）以及Kolmogorov-Smirnov 檢定（K-S test），A-D test 的檢定力普遍比K-S test 強，因其對分配的尾端較為敏感，但K-S test 執行起來較為簡單，亦可廣泛地延伸至多變量分配。本文主要是根據K-S test 的概念，定義一個稱為Lp-norm 的K-S 檢定統計量來執行連續型分配的適合度檢定。此方法可運用到單一變量及多變量分配的檢定，在電腦模擬的實驗下本文也證明所提方法於某些參數設定之下有較高的檢定力。 zh_TW dc.description.tableofcontents 第一章 前言與文獻探討 1第二章 檢定方法介紹 52.1 單變量適合度檢定 52.1.1 Kolmogorov-Smirnov檢定 52.1.2 Anderson-Darling檢定 82.2 多變量Kolmogorov-Smirnov檢定 102.3 以Lp-norm為基準之Kolmogorov-Smirnov檢定 142.3.1 針對單變量之Lp-norm K-S檢定 142.3.2 針對多變量之Lp-norm K-S檢定 16第三章 模擬評估各檢定之表現 183.1 單變量適合度檢定 183.1.1 Location family的檢定 183.1.2 Scale family的檢定 263.2 雙變量適合度檢定 313.2.1 Location family的檢定 313.2.2 Scale family的檢定 37第四章 結論 43參考文獻 45 zh_TW dc.format.extent 3385358 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106354017 en_US dc.subject (關鍵詞) 適合度檢定 zh_TW dc.subject (關鍵詞) 經驗分佈函數 zh_TW dc.subject (關鍵詞) 卡方適合度檢定 zh_TW dc.subject (關鍵詞) Anderson-Darling檢定 zh_TW dc.subject (關鍵詞) Kolmogorov-Smirnov檢定 zh_TW dc.title (題名) 以經驗分佈函數為基準之適合度檢定方法 zh_TW dc.title (題名) Alternative Goodness-of-Fit Tests based on Empirical Distribution en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 1. Alodat, M.T., Al-Subh, S.A., Ibrahim K., & Jemain A.A. (2010). “EmpiricalCharacteristic Function Approach to Goodness of Fit Tests for the LogisticDistribution under SRS and RSS”, Journal of Modern Applied Statistical Methods,Vol. 9, No. 2, 558-567.2. Bakshaev, A., & Rudzkis, R. (2015). “Multivariate goodness-of-fit tests based onkernel density estimators”, Nonlinear Analysis: Modelling and Control, Vol. 20, No.4, 585-602.3. Chen, W.C., Hung, Y.C., & Balakrishnan N. (2014) “Generating beta randomnumbers and Dirichlet random vectors in R: The package rBeta2009”,Computational Statistics and Data Analysis, 71, 1011-1020.4. Facchinetti, S. (2009) “A Procedure to Find Exact Critical Values of Kolmogorov-Smirnov test”, Statistica Applicata – Italian Journal of Applied Statistics, Vol. 21,No. 3-4, 337-359.5. Hung, Y.C., & Chen W.C. (2017). “Simulation of some multivariate distributionsrelated to Dirichlet distribution with application to Monte Carlo simulations”,Communication in Statistics-Simulation and Computation, Vol. 46, No. 6, 4281-4296.6. Justel, A., Pena, D., & Zamar, R. (1997). “A Multivariate Kolmogorov-SmirnovTest of Goodness of Fit”, Statistics and Probability Letters, 35, 251-259.7. McAssey, M.P. (2013) “An empirical goodness-of-fit test for multivariatedistributions’, Journal of Applied Statistics, 40:5, 1120-1131.8. Mirhossini, S.M., Amini M., & Dolati A. (2015) “On a general structure of bivariateFGM type distributions”, Application of Mathematics, Vol. 60, No. 1, 91-108.9. Razali , N.M., & Wah, Y.B. (2011) “Power comparisons of Shapiro-Wilk,Kolmogorov-Smirnov, Lillefors and Anderson-Darling tests”, Journal of StatisticalModeling and Analytics, Vol.2, No. 1, 21-33.10. R package “Emcdf” (2018). URL: https://cran.r-project.org/web/packages/Emcdf/index.html.11. R package “MultiRNG” (2019). URL: https://cran.r-project.org/web/packages/MultiRNG/index.html.12. R package “pbivnorm” (2015). URL: https://github.com/brentonk/pbivnorm.13. Stephens M.A. (1974). “EDF Statistics of Goodness of Fit and Some Comparisons”,Journal of the American Statistical Association, Vol. 69, No.347, 730-737.14. Vaidyanathan, V.S., & Varghese, S. (2016) “Morgenstern type bivariate Lindleydistribution”, Statistics, Optimization and Information Computing, Vol. 4, 132-146.15. Yang, G.Y. (2012). “The Energy Goodness-of-Fit Test for Univariate StableDistributions”. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202000071 en_US
