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題名 事故傾向服從Inverse Gaussian分配時混合Weibull模式之研究
作者 黃(糸秀)琪
Huang, Hsiu-Chi
貢獻者 陳麗霞
Chen,Li-Shya
黃(糸秀)琪
Huang,Hsiu-Chi
關鍵詞 成群資料
存活分析
群內相關
事故傾向
Weibull迴歸模式
Inverse Gaussian分配
分數檢定
Group Data
Survival Analysis
Within Correlation
Frailty
Weibull Regression Model
Inverse Gaussian Distribution
Score Test
日期 2001
上傳時間 15-四月-2016 16:10:27 (UTC+8)
摘要 本篇論文主要考慮成群資料的存活分析，其特點為群內個體間具有相關性，並假定群內個體具有相同但無法觀測到的事故傾向。首先，探討事故傾向服從任一連續分配時混合Weibull迴歸模式的特性，接著，推導出事故傾向服從血Inverse Gaussian吧時之混合Weibull模式，並介紹參數的估計問題。然後，推導出群內個體是否獨立之分數檢定統計量，以分別就兩種最常見的存活資料型態一完整型態與右設限型態：檢定模式中事故傾向的效應是否存在。最後，並以實例說明分數檢定之程序。
In this paper, we study survival analysis for grouped data, where the within group correlations are considered. It is also assumed that individuals within the same group share a common but unobservable random frailty. First, we discuss the properties of the Weibull regression model mixed by any continuous distribution. Next, we derive an Inverse Gaussan mixture of Weibull regression model, and discuss the estimation problem. Then, we derive the score test for testing independence between components within the same group, where the two most common cases are discussed the complete data case and the right censoring case. Finally, the testing procedures are illustrated by two examples.
參考文獻 Aalen, O. O. (1994). "Effects of frailty in survival analysis." Statistical Method in Medical Research 3, 227-243.
Bernardo, J. M. (1976). "Algorithm AS 103: Psi (Digamma) function." Applied Statistics 25, 315-317.
Clayton, D. (1978). "A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence." Biometrika 65,141-151.
Commenges, D. and Andersen, P. K. (1995). "Score test of homogeneity for survival data." Lifetime Data Analysis 1,145-156.
Crowder, M. J., Kimber, A. C., Smith, R. L. and Sweeting, T. J. (1991). Statistical Analysis of Reliability Data. Chapman & Hall, London.
Crowder, M. J. and Kimber, A. C. (1997). "A score test for the multivariate Burr and other weibull mixture distributions." Scandinavian Journal of Statistics, Theory and Applications 24, 419-432.
Hougaard, P. (1986a). "Survival models for heterogeneous populations derived from stable distributions." Biometrika 73, 387-396.
Hougaard, P. (1986b). "A class of multivariate failure time distributions." Biometrika 73, 671-678.
Kimber, A. C. (1996). "A weibull-based score test for heterogeneity." Lifetime Data Analysis 2, 63-71.
Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York.
Lee, M.-L. T. (1985). "Dependence by total positivity." The Annals of Probability 13, 572-582.
Moore, R. J. (1982). "Algorithm AS 187: Derivatives of the incomplete gamma integral." Applied Statistics 31, 330-335.
Pierce, D. A. (1982). "The asymptotic effect of substituting estimators for parameters in certain types of statistics." The Annals of Statistics 10, 475-478.
Sahu, S. K., Dey, D. K., Aslanidou, H. and Sinha, D. (1997). "A weibull regression model with gamma frailties for multivariate survival data." Lifetime Data Analysis 3, 123-137.
Schneider, B. E. (1978). "Algorithm AS 121: Trigamma function." Applied Statistics 27, 97-99.
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. John Wiley & Sons, New York.
Tweedie, M. C. K. (1957). "Statistical properties of inverse gaussian distributions. I." The Annals of Mathematical Statistics 28, 362-377.
Venables, W. N. and Ripley, B. D. (1994). Modern Applied Statistics with S-Plus. Springer-Verlag, New York.
Whitmore, G. A. and Lee, M.-L. T. (1991). "A multivariate survival distribution generated by an inverse gaussian mixture of exponentials." Technometrics 33, 39-50.
描述 碩士
國立政治大學
統計學系
87354020
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001360
資料類型 thesis
dc.contributor.advisor 陳麗霞zh_TW
dc.contributor.advisor Chen,Li-Shyaen_US
dc.contributor.author (作者) 黃(糸秀)琪zh_TW
dc.contributor.author (作者) Huang,Hsiu-Chien_US
dc.creator (作者) 黃(糸秀)琪zh_TW
dc.creator (作者) Huang, Hsiu-Chien_US
dc.date (日期) 2001en_US
dc.date.accessioned 15-四月-2016 16:10:27 (UTC+8)-
dc.date.available 15-四月-2016 16:10:27 (UTC+8)-
dc.date.issued (上傳時間) 15-四月-2016 16:10:27 (UTC+8)-
dc.identifier (其他 識別碼) A2002001360en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85147-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 87354020zh_TW
dc.description.abstract (摘要) 本篇論文主要考慮成群資料的存活分析，其特點為群內個體間具有相關性，並假定群內個體具有相同但無法觀測到的事故傾向。首先，探討事故傾向服從任一連續分配時混合Weibull迴歸模式的特性，接著，推導出事故傾向服從血Inverse Gaussian吧時之混合Weibull模式，並介紹參數的估計問題。然後，推導出群內個體是否獨立之分數檢定統計量，以分別就兩種最常見的存活資料型態一完整型態與右設限型態：檢定模式中事故傾向的效應是否存在。最後，並以實例說明分數檢定之程序。zh_TW
dc.description.abstract (摘要) In this paper, we study survival analysis for grouped data, where the within group correlations are considered. It is also assumed that individuals within the same group share a common but unobservable random frailty. First, we discuss the properties of the Weibull regression model mixed by any continuous distribution. Next, we derive an Inverse Gaussan mixture of Weibull regression model, and discuss the estimation problem. Then, we derive the score test for testing independence between components within the same group, where the two most common cases are discussed the complete data case and the right censoring case. Finally, the testing procedures are illustrated by two examples.en_US
dc.description.tableofcontents 封面頁
證明書
致謝詞
論文摘要
目錄
第一章 緒論
1-1節 研究動機及目的
1-2節 文獻回顧
1-3節 論文架構
第二章 混合Weibull模式之介紹
2-1節 混合Weibull迴歸模式
2-2節 以Inverse Gaussian分配混合Weibull迴歸模式之介紹
2-3節 參數估計
第三章 群內個體互為獨立之檢定
3-1節 完整型態資料
3-1-1節 干擾參數為已知
3-1-2節 干擾參數為未知
3-2節 包含右設限型態資料
3-3節 實例分析
3-3-1節 實例一
3-3-2節 實例
第四章 結論與建議
4-1節 結論
4-2節 未來研究方向
參考文獻
附錄
附錄一：纖維承受扯力資料
附錄二：飛機空調系統運作時間資料
附錄三：實例一資料分析程式
附錄四：實例二資料分析程式		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001360en_US
dc.subject (關鍵詞) 成群資料zh_TW
dc.subject (關鍵詞) 存活分析zh_TW
dc.subject (關鍵詞) 群內相關zh_TW
dc.subject (關鍵詞) 事故傾向zh_TW
dc.subject (關鍵詞) Weibull迴歸模式zh_TW
dc.subject (關鍵詞) Inverse Gaussian分配zh_TW
dc.subject (關鍵詞) 分數檢定zh_TW
dc.subject (關鍵詞) Group Dataen_US
dc.subject (關鍵詞) Survival Analysisen_US
dc.subject (關鍵詞) Within Correlationen_US
dc.subject (關鍵詞) Frailtyen_US
dc.subject (關鍵詞) Weibull Regression Modelen_US
dc.subject (關鍵詞) Inverse Gaussian Distributionen_US
dc.subject (關鍵詞) Score Testen_US
dc.title (題名) 事故傾向服從Inverse Gaussian分配時混合Weibull模式之研究zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Aalen, O. O. (1994). "Effects of frailty in survival analysis." Statistical Method in Medical Research 3, 227-243.
Bernardo, J. M. (1976). "Algorithm AS 103: Psi (Digamma) function." Applied Statistics 25, 315-317.
Clayton, D. (1978). "A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence." Biometrika 65,141-151.
Commenges, D. and Andersen, P. K. (1995). "Score test of homogeneity for survival data." Lifetime Data Analysis 1,145-156.
Crowder, M. J., Kimber, A. C., Smith, R. L. and Sweeting, T. J. (1991). Statistical Analysis of Reliability Data. Chapman & Hall, London.
Crowder, M. J. and Kimber, A. C. (1997). "A score test for the multivariate Burr and other weibull mixture distributions." Scandinavian Journal of Statistics, Theory and Applications 24, 419-432.
Hougaard, P. (1986a). "Survival models for heterogeneous populations derived from stable distributions." Biometrika 73, 387-396.
Hougaard, P. (1986b). "A class of multivariate failure time distributions." Biometrika 73, 671-678.
Kimber, A. C. (1996). "A weibull-based score test for heterogeneity." Lifetime Data Analysis 2, 63-71.
Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York.
Lee, M.-L. T. (1985). "Dependence by total positivity." The Annals of Probability 13, 572-582.
Moore, R. J. (1982). "Algorithm AS 187: Derivatives of the incomplete gamma integral." Applied Statistics 31, 330-335.
Pierce, D. A. (1982). "The asymptotic effect of substituting estimators for parameters in certain types of statistics." The Annals of Statistics 10, 475-478.
Sahu, S. K., Dey, D. K., Aslanidou, H. and Sinha, D. (1997). "A weibull regression model with gamma frailties for multivariate survival data." Lifetime Data Analysis 3, 123-137.
Schneider, B. E. (1978). "Algorithm AS 121: Trigamma function." Applied Statistics 27, 97-99.
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. John Wiley & Sons, New York.
Tweedie, M. C. K. (1957). "Statistical properties of inverse gaussian distributions. I." The Annals of Mathematical Statistics 28, 362-377.
Venables, W. N. and Ripley, B. D. (1994). Modern Applied Statistics with S-Plus. Springer-Verlag, New York.
Whitmore, G. A. and Lee, M.-L. T. (1991). "A multivariate survival distribution generated by an inverse gaussian mixture of exponentials." Technometrics 33, 39-50.		zh_TW