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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/87861
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/87861


    Title: 兩母體生存函數比較之研究
    To study about the comparing two population`s survival functions
    Authors: 傅鼎傑
    Ting, Chieh Fu
    Contributors: 陳麗霞
    Chen Li Hsia
    傅鼎傑
    Ting,Chieh Fu
    Keywords: 生存函數
    Kaplan-Meier估計量
    An假設
    Berliner-Hill估計量
    Gehan-Wilcoxon檢定
    Cox-Mantel檢定
    修飾型的Kolmogorov-Smirnov檢定
    Bootstrap方法
    survival function
    An assumption
    Berliner-Hill estimator
    Gehan-Wilcoxon test
    Kaplan-Meier
    Date: 1994
    Issue Date: 2016-04-29 09:20:55 (UTC+8)
    Abstract:   對於生存時間的資料而言,通常我們所想要研究瞭解的是,至少存活到某特定時間點的機率,而這個機率亦即生存分析中的生存函數(survival function)。當有兩個不同的母體存在時,為了要知道這兩個母體的生存函數是否相同,在統計方法上,我們將進行一些檢定,常用的有Gehan-Wilcoxon和Cox-Mantel之兩樣本檢定,後來又有修飾型的Kolmogorov-Smirnov檢定。但是,前兩種檢定方法,只對此兩組生存函數呈現某特殊型式時,具有好的檢定力。因此,透過一些實證的研究,將上述檢定方法做有系統的整理,進而發展出一套簡單又有效率的檢定程序。再者,若檢定得此兩個母體之生存函數不相等時,如何利用Bootstrap方法,進一步對兩組生存函數之特定生存機率點或生存時間點所分別對應之生存時間或生存機率差距做推論與比較,本文將有詳細她說明;以提供研究人員更多有效的資訊,不再僅止於檢定虛無假設是否拒絕而已。最後,我們又藉由推廣上述Bootstrap方法,將其運用到檢定方法上,而另外發展出一種新的兩母體生存函數之檢定方法。
      When two different populations exist, we will take some tests by Cehan-Wilcoxon, Cox-Mantel or Modified Kolmogorov- Smirnov in satistical way. Therefore we develope a simple and efficient test process from arranging above test ways system- atically through some real study. How to use Bootstrap way to infer the difference of survival time or survival probability of specular point. We infer Bootstrap way on test work and then develope a new two populations survival function test way.
    Reference: Akritas, M.G.(1986), "Empirical Process Associated with v-statistics and a class of estimators under random censoring", the annals of statistics, 14, 619-637.
    Cox, D. R (1959), "The analysis of exponentially distributed life-times with two types of failures", journal of the royal statistical society, series B, 21, 411-421
    Mantel, N, (1977), "test and limts for the common odds ratio of several 2x2 contingency tables: methods in analogy with the mantel-haenszel procedure", jornal of statistical planning, 1, 179-189.
    Romano, Siegel, (1991), "Counterexamples in probability & statistics-the two sample case", annals of mathematical statistics, 27, 590-615.
    Schey, H.M(1977), "the asymptotic distrubution of the one-sided kolmogorovsmirnov statistic for truncated data", communications in statistics A6, 1361-1365
    Tarone, R.E. and Ware, J (1977), "On Distrubtion-free Tests for Equality of Survival Distributation", Biometrica, 64, 156-160.
    Description: 碩士
    國立政治大學
    統計學系
    82354007
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002003383
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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