基於Hellinger最短距離法之韋伯模型的參數估計

Inferences for Weibull Model on minimum Hellinger distance

廖淑蓉(Shu-Rong Liao)

指導教授 ： 黃文濤

淡江大學/管理學院/管理科學研究所碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00433

摘要

韋伯分配分佈已廣泛應用於許多領域，尤其是可靠度分析及產品的壽命分析等，是所有分配中較符合浴缸型分配，並且估計其參數是一個重要的問題，因此考慮到估計問題。
　　但是，當資料的數據是受污染的情況，估計其參數不具穩健性。在此論文中，吾人針對此問題運用minimum Hellinger distance estimate (MHDE)估計參數。眾所周知，MHDE不僅具有效性，且具有穩健性，還提供了數值模擬的基礎上最大概似估計法和MHDE及其比較。
　　最後，提出一些延伸的Weibull模型，推廣成四個參數型態之分配。

關鍵字

韋伯模型 ； 海林格最短距離 ； 高斯核函數

並列摘要

Weibull distribution has been widely applied in many areas and estimations of its parameters are an important issue. Thus are let of literature. Consider the estimation problem; however, when the data is contaminated most of the proposed estimations do not possess the property of robustness. In this thesis, we apply minimum Hellinger distance estimate (MHDE) for this problem. As is well-known, MHDE provides not only the first order efficiency, but also robustness, we have also provided numerical simulations based on MLE and MHDE and its comparisons have been made.
Finally, some extension of the Weibull model has also been proposed.

並列關鍵字

Weibull distribution ； Minimum Hellinger distance ； Gauss Kernel function

參考文獻

[1] Ahmad, I. A. and Fan, Y. (2001) , “Optimal bandwidth for kernel density estimators of functions of Observations, ”Statistics and Probability Letter, 513, 245-251.

[2] B. U. Park and W. C. Kim (1994) , “Asymptotically best bandwidth selectors in kernel density estimation ,”Statistics and Probability Letters, 19, 119-127.

[3] Balakrishnan, N. and Kocherlakota, S. (1985) , “On the double Weibull distribution: Order statistics and estimation ,”Sankhya, 47, 161-176.

[4] Basu, A., and Lindsay, B. G. (1994) , “Minimum Disparity Estimation for Continuous Models :Efficiency, Distributions and Robustness ,”Annals of the Institute of Statistical Mathematics,46, 638-705.

[5] Beran, R. J. (1977) , “Minimum Hellinger Distance Estimates for Parametric Models ,”The Annals of Statistics, 5, 445-463.