一維及二維右設限存活資料的適合度檢定

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李念純(Nien-chun Li) 查詢紙本館藏

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統計研究所

論文名稱

一維及二維右設限存活資料的適合度檢定
(Goodness-of-fit tests for univariate and bivariate right censored survival data)

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摘要(中)

分析資料的統計方法有兩類：一種是無母數方法，另一種是有母數方法。雖然資料用無母數方法分析可以不假設任何特定的母體分布，但正確的使用有母數方法可以獲取較多的資訊。為能正確使用有母數方法，就必須根據資料建立分布的適合度檢定。本文分別在完整或右設限的一維度資料之下修正Kolmogorov和Cramer-von Mises統計式，在成對資料之下推廣修正Kolmogorov和Chi-square統計式進行資料分布的適合度檢定，此處的一維度資料考慮配適廣義伽瑪分布，成對資料則針對關聯結構函數做適合度檢定。本文以模擬的方法研究所提出適合度檢定的型I誤差率及檢定力的表現，最後以實例說明所提出檢定方法之應用。

摘要(英)

There are two kinds of statistical methods for analyzing data: one is the nonparametric analysis and the other is the parametric analysis. We do not need to assume any particular form for the population distribution when we use a nonparametric method, however, correctly using a parametric method would produce more information on data analysis. To do so, we need to test the goodness-of-fit of a particular distribution based on the available data. In this paper, we construct goodness-of-fit tests for univariate and bivariate observations, respectively, with completely observed or right-censored data. Modifications of the Kolmogorov and Cramer-von Mises tests are proposed for testing the goodness-of-fit of the generalized gamma distribution for univariate data. Extensions of the Kolmogorov and Chi-square tests to testing the goodness-of-fit of a Copula function for bivariate data are then suggested. The results of a simulation study are presented for the investigation of type I error rates and powers of the proposed tests. Finally, the application of the tests is illustrated by using a real data set.

關鍵字(中)

★ 適合度檢定
★ 右設限
★ Kolmogorov
★ Cramer-von Mises
★ 關聯結構函數
★ Chi-square

關鍵字(英)

★ goodness-of-fit test
★ Chi-square
★ right-censored
★ Kolmogorov
★ Cramer-von Mises
★ copula function

論文目次

摘要 i
Abstract ii
誌謝辭 iii
目錄 v
圖目錄 vi
表目錄 vii
第一章研究動機及目的 1
第二章文獻回顧 5
2.1 Lillierfors 5
2.2 估計聯合存活函數 6
2.3 關聯結構函數 8
2.4 卡方統計式 10
2.5 右偏分布 12
第三章統計方法 14
3.1 一維資料的適合度檢定 14
3.2 二維資料的適合度檢定 16
第四章模擬研究 20
4.1 模擬方法 20
4.2 模擬結果 22
第五章實例分析 25
5.1 霍奇金疾病 25
5.2 愛滋病患者 26
5.3 喉癌 26
5.4 燒燙傷病患 27
第六章結論與討論 29
參考文獻 31
附錄 34

參考文獻

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指導教授

陳玉英(Yuh-ing Chen)

審核日期

2011-7-1

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