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系統識別號 U0002-2006200510131000
中文論文名稱 二元分佈族及其統計推論
英文論文名稱 A Family of Bivariate Distributions With Some Applications to Statistical Inferences
校院名稱 淡江大學
系所名稱(中) 管理科學研究所碩士班
系所名稱(英) Graduate Institute of Management Science
學年度 93
學期 2
出版年 94
研究生中文姓名 邱全宏
研究生英文姓名 Chuan-Hung Chiu
學號 692560450
學位類別 碩士
語文別 中文
口試日期 2005-06-13
論文頁數 30頁
口試委員 指導教授-黃文濤
委員-賴耀宗
委員-吳錦全
中文關鍵字 二元分佈族  二元指數分佈  二元韋伯分佈  S-N曲線  隨機疲勞極限  誤差測量迴歸模型 
英文關鍵字 Family of bivariate distributions  bivariate exponential  bivariate Weibull  S-N curve  random fatigue-limit  error in measurement 
學科別分類 學科別社會科學管理學
中文摘要 在第一章,我們提出了一個新的二元分佈族,並提供一些特殊之分佈,如二元指數、二元韋伯等,同時並與已知的二元分佈族做些比較。對於一些相關之統計性質,如期望值、變異數、故障函數等,及參數的估計也作了探討。並舉一實例,應用動差法,估算出其參數值。
在第二章,對於S-N曲線的建立提供了另一種統計模式,並估計模型中的參數,同時考慮測量誤差的迴歸模型方法,以導出疲勞極限的分佈。在此分佈下,以迴歸分析法導出參數的估計。此外,亦提出一實際之實驗數據,以本文方法算出參數的估計值,並與已知的結果比較。最後,進行統計模擬研究。
英文摘要 In chapter 1, we have proposed a new family of bivariate distributions, and also some special distributions such as bivariate exponential, bivariate Weibull etc.. Some comparisons with known results are also made. A real data set is illustrated in which some parameters are estimated by moment method.
In chapter 2, we consider an error-in-variables regression model for random fatigue-limit problem. Some estimates for the related parameters are also derived. A real data set is also illustrated by the proposed method and some comparisons are also made with known results. Some simulation study is also carried out.
論文目次 第一章 二元分佈族…………………………………………………..1
1.1 介紹……………………………………………………………….1
1.1.1背景………………………………………………………………1
1.1.2 多元分佈的相關文獻………………………...............2
1.2 一些相關定義及符號…………………………...............3
1.3 二元分佈族……………………………………………………….4
1.3.1二元分佈族與其他相關的二元分佈......................4
1.3.2二元分佈之模型比較………………………………………….10
1.3.3二元分佈的參數估計.................................12
1.4 實例………………………………………………………………15
1.5 結論………………………………………………………………16
第二章 隨機疲勞極限模型………………………………………….18
2.1介紹……………………………………………………………….18
2.1.1 背景……………………………………………………………18
2.1.2 相關的文章……………………………………………………18
2.2 疲勞模型…………………………………………………………19
2.2.1相關符號與定義……………………………………………….19
2.3實例……………………………………………………………….21
2.4與其他的疲勞模型作比較……………………………………...22
2.5 模擬………………………………………………………………23
2.6 結論………………………………………………………………25
參考資料………………………………………………………………26

表目錄:
表一 皮膚燒傷移植手術之生存日數..........................15
表二 疲勞實驗數據資料………………………………………………22
表三 比較各模型的絕對值殘差………………………………………23
表四 模擬結果…………………………………………………………24
參考文獻 [1]Balakrishnan, N., Castillo, E. and Sarabia, J.M. (2004),”Bivariate Continuous Distributions with Specified Conditional Hazard Functions,” private communications.
[2]Bastenaire, F. A. (1972), ”New method for the statistical evaluation of constant stress amplitude fatigue-test results,” in Probability Aspects of Fatigue (ASTM STP 511), ed. R. A. Heller, Philadelphia: American Society for Testing and Materials, 3-28.
[3]Castillo, E., Fernaadez-Canteli, A., Esslinger, V., and Thurlimann, B. (1985),”Statistical model for fatigue analysis of wires. Strands and cables,” in International Association for Bridge And Structural Engineering Proceedings P-82/85, Zurich, International Association for Bridge And Structural Engineering, 1-40.
[4]Castillo, E. and Hadi, A.S. (1995),”Modeling Lifetime Data with Application to Fatigue Model,” Journal of the American Statistical Association, 90, 1041-1054.
[5]Clayton, D. and Cuzick, J. (1985),”Multivariate Generalizations of The Proportional Hazards Model,” Journal of the Royal Statistical Society Series A, 148, 82-117.
[6]Finkelstein, M.S. (2003), “On One Class of Bivariate Distributions”, Statistics & Probability Letters, 65, 1-6.
[7]Fuller, W.A. (1987), Measurement Error Models, John Wiley & Sons.
[8]Gumbel, E.J (1960),”Bivariate Exponential Distributions,” Journal of the American Statistical Association, 55, 698-707.
[9]Kotz, S., Balakrishnan, N., Johnson, N. S. and (2000),”Continuous Multivariate Distributions,” Vol. 1, second edition, John Wiley & Sons.
[10]Little, R. E., and Ekvall, J. C. (eds.) (1981), Statistical Analysis of Fatigue Data (ASTM STP 744), Philadelphia:The American Society for Testing and Materials.
[11]Pascual, F.G. and Meeker, W.Q. (1999),”Estimating Fatigue Curves with the Random Fatigue-limit Model,” Technometrics, 41, 277-302.
[12]Pascual, F.G. (2003), “The Random Fatigue-limit Model in Multi-factor Experiment,” Journal of Statistical Computation and Simulation, 10, 733-752.
[13]Spindel, J. E. and Haibach, E. (1981), ”Some considerations in the statistical determination of the sharp of the S-N curves,” in Statistical Analysis of Fatigue Data (ASTM STP 744),eds. Little, R. E., and Ekvall, J. C., Philadelphia:The American Society for Testing and Materials, 89-113.
[14]Woolson, R. F. and Lachenbruch, P. A. (1980), ”Rank test for censored matched pairs,” Biometrika, 67, 597-606.
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