陳氏分佈族之統計推論

Inferences of Chen’s family

葉純志(Chun-Chih Yeh)

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.2009.00331

摘要

陳氏於2000年時提出了一個大的分佈族，其故障率函數呈現浴缸形分佈，不幸的是這個參數估計並非真正的最大概似估計量。因此，本文中提出了最短Hellinger距離來估計參數。最短Hellinger 距離擁有一些好的特性，它不僅擁有有效性還具有穩健性的特性。當數據資料受到汙染，穩健性的估計是一個適當的選擇。在數值模擬時將分別針對最大概似估計量與最短Hellinger 距離進行參數估計，並建議參數估計的方法。
最後推廣陳氏模型，並針對推廣模型進行檢定。

關鍵字

核函數 ； 最短距離 ； 浴缸型

並列摘要

Chen (2000) proposed a big family of distributions which is suitable for life model since its hazard rate function has a bathtub shape. Unfortunately, the proposed estimate for the parameter is not an exact MLE. In this thesis, we propose the minimum Hellinger distance estimate (MHDE) for the parameters involved in the family. This MHDE has good properties; it possesses not only the first order efficiency, but also robustness. When the data is contaminated, robust estimate is an appropriate choice. Some numerical simulations have been carried out both for the case of maximum likelihood like estimate and MHDE. Some improved estimate has been proposed.
Finally, some extension of the Chen’s model has also been made.

並列關鍵字

kernel ； minimum Hellinger distance ； bathtub

參考文獻

[1] Beran, R., 1997, Minimum Hellinger distance estimates for parameteric models, The Annals of Statistics, 5(3), 445-463.

[2] Chen Z., 2000, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, 49,155-161.

[6] Devroye, L., 1989, The double kernel method in density estimation, Ann. Inst. Henri Poincare, 25, 533-580.

[7] Hall, P. and Wand, M.P., 1988a, Minimizing L1 distance in nonparameteric density estimation, Journal of Multivariate Analysis, 26, 59-88.

[8] Hall, P. and Wand, M.P., 1988b, On the minimization of absolute distance in kernel density estimation, Statistics & Probability Letters, 6 311-314.