二元分佈族及其統計推論

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。

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

並列摘要

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.

並列關鍵字

Family of bivariate distributions ； bivariate exponential ； bivariate Weibull ； S-N curve ； random fatigue-limit ； error in measurement

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.

[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.

國際替代計量

二元分佈族及其統計推論

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