博碩士論文 100225018 詳細資訊




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姓名 徐紹凱(Shau-Kai Shiu)  查詢紙本館藏   畢業系所 統計研究所
論文名稱
(Estimation and model selection for left-truncated and right-censored data: Application to power transformer lifetime modeling)
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摘要(中) 電力變壓器壽命資料經常發生左截略(left truncation)與右設限(right censoring)的情況。Balakrishnan and Mitra (2011 JSPI, 2012 CSDA)針對截略與設限資料,分別以對數常態(lognormal)與韋伯(Weibull)為模型,提出利用最大期望演算法(EM algorithm)得到最大概似估計量(maximum likelihood estiamtion)。我們以模擬研究來顯示牛頓-拉弗森演算法(Newton-Raphson algorithm)與最大期望演算法在參數估計上的優劣。我們發現以對數常態分配為模型,當樣本數較小與設限比率較高時,使用牛頓法估計參數容易發生發散的情形。然而,在樣本數較大的情況下,牛頓法比最大期望演算法有較快的收斂速度並能得到較準確的估計量。另外,我們使用赤池信息量準則(Akaike’s information criterion)來選擇最合適的模型。
摘要(英) Left truncation and right censoring often occurs in power transformer lifetime data. Suitably adjusted for censoring and truncation, the maximum likelihood estimation has been proposed with the EM algorithm under the lognormal and Weibull models (Balakrishnan and Mitra, 2011 JSPI, 2012 CSDA). In this thesis, we compare the performance of the Newton-Raphson algorithm with their EM algorithm by simulations. Our comparison based on Monte Carlo simulations shows that the Newton-Raphson method for lognormal distribution fails to converge frequently when the sample size is small and the percentage of censoring is high. However, we observe that the Newton-Raphson method has a faster rate of convergence and give more accurate standard error estimates than the EM with missing information principle for moderate sample sizes. In addition, we examine the performance of the Akaike’s information criterion (AIC) for selecting a best distribution among candidate models. Finally, these methods discussed here are illustrated through real data examples.
關鍵字(中) ★ 左截略
★ 右設限
★ 對數常態分佈
★ 韋伯分佈
★ 牛頓-拉弗森演算法
★ 最大期望演算法
★ 赤池信息量準則
關鍵字(英) ★ Left truncation
★ right censoring
★ lognormal distribution
★ Weibull distribution
★ Newton-Raphson algorithm
★ EM algorithm
★ Akaike’s information criterion
論文目次 摘要 I
Abstract II
誌 謝 III
List of Table VI
List of Figure VIII
Chapter 1 Introduction 1
Chapter 2 Left-truncated and right-censored data 3
Chapter 3 Methods of estimation 5
3.1 Likelihood functions 5
Example 1: Lognormal distribution 6
Example 2: Weibull distribution 7
Example 3: Exponential distribution 8
3.2 Newton-Raphson method 8
3.2.1 Lognormal distribution 9
3.2.2 Weibull distribution 10
3.2.3 Exponential distribution 11
3.3 The EM algorithm 12
Example 4: Lognormal distribution 12
Example 5: Weibull distribution 14
Chapter 4 Model selection 17
Chapter 5 Simulations 18
5.1 Simulation design 18
5.2 Simulation results for the lognormal distribution 19
5.3 Simulation results for the Weibull distribution 25
5.4 Model selection by AIC 27
Chapter 6 Data analysis 31
6.1 Transformer lifetime data 31
6.2 Data from Balakrishnan and Mitra (2012) 33
Chapter 7 Conclusion and Discussion 35
Appendix 37
Appendix I Checking the MLE of the exponential distribution with parameter 37
Appendix II EM methods for lognormal distribution 37
Appendix III EM gradient algorithm for Weibull distribution 39
Appendix IV Changing the stopping criterion 41
References 44
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Ng, H.K.T., Chan, P.S., Balakrishnan, N, 2002. Estimation of parameters from progressively censored data using EM algorithm. Computational Statistics & Data Analysis 39, 371-386.
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指導教授 江村剛志(Takeshi Emura) 審核日期 2013-6-26
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