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    题名: 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
    贡献者: 洪英超
    Hung, Ying-Chao
    許晉瑋
    Hsu, Chin-Wei
    关键词: 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
    上传时间: 2020-02-05 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). “Empirical
    Characteristic Function Approach to Goodness of Fit Tests for the Logistic
    Distribution 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 on
    kernel 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 random
    numbers 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 distributions
    related 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-Smirnov
    Test of Goodness of Fit”, Statistics and Probability Letters, 35, 251-259.
    7. McAssey, M.P. (2013) “An empirical goodness-of-fit test for multivariate
    distributions’, Journal of Applied Statistics, 40:5, 1120-1131.
    8. Mirhossini, S.M., Amini M., & Dolati A. (2015) “On a general structure of bivariate
    FGM 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 Statistical
    Modeling 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 Lindley
    distribution”, Statistics, Optimization and Information Computing, Vol. 4, 132-146.
    15. Yang, G.Y. (2012). “The Energy Goodness-of-Fit Test for Univariate Stable
    Distributions”.
    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
    数据类型: thesis
    DOI: 10.6814/NCCU202000071
    显示于类别:[統計學系] 學位論文

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