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研究生: 江峰政
Chiang, Feng-Cheng
論文名稱: 有關EM法於具韋伯之設限資料其參數之估計
Weibull-Parameters Estimation with Censored Type Data Using Generalized EM Algorithm
指導教授: 陳重弘
Chen, Chong-Hong
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2005
畢業學年度: 93
語文別: 中文
論文頁數: 60
中文關鍵詞: 循序性設限資料EM 演算法ECME 演算法韋伯分配
外文關鍵詞: EM algorithm, Weibull distribution, ECME algorithm, progressive censored data
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  • 韋伯分配在存活分析和可靠度分析中是常被使用到的分配,而循序性設限資料在其中更是不可或缺的資料型態之一,因此本文以韋伯分配下的循序性設限資料為模型。再利用 EM演算法及其延伸ECM演算法和ECME演算法來做估計,並利用其參數之變異數及收斂速度矩陣的特徵值大小來比較其之間的優劣。在模擬結果中,發現ECME的收斂速度總是比EM的收斂速度快,且ECME的變異數都比EM的變異數來得小,因此ECME整體而言是較好的。

    Weibull distribution is a distribution often used in survival analysis and reliability analysis. And progresssive censored data is a vital one of data types. In this article, the model we take is the progressive censored data in Weibull distribution. And we use the EM algorithm and it's extension, ECM and ECME, to estimate the parameters. Final, we compare EM and ECME by using the variances of parameters and the e-igenvalues of matr-
    ix speed of convergence. In the simulation, we can find the speed of convergence of ECME is always faster than this of ECM. And the variance of ECME is smaller than the variance of EM, so ECME is the better method.

    1 緒論 3 2 模式分析 4 2.1 韋伯分配及其性質 4 2.2 循序性型二右設限資料 6 3 EM演算法及其延伸(ECM、ECME ) 9 3.1 EM演算法 9 3.2 ECM演算法 12 3.3 ECME演算法 13 4 估計 16 4.1 EM演算法 16 4.2 ECM演算法 22 4.3 ECME演算法 22 4.4 變異數及共變異數 24 4.5 收斂速率矩陣 27 5 模擬 29 5.1 模擬方式 29 5.2 模擬結果 30 6 結論 49 參考文獻 50 附錄 52

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