在逐步型Ⅱ設限與一般化逐步型Ⅱ設限下使用 一些新的樞紐量對Gompertz分配與極值分配做統計推論

Using Some New Pivotal Quantities to Do Statistical Inferencesfor the Gompertz Distribution and the Extreme-Value Distribution under Progressive Type II Censoring and General Progressive Type II Censoring

蘇均哲(Chun-Che Su)

指導教授 ： 吳淑妃

淡江大學/管理學院/統計學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00909

摘要

在壽命試驗研究中，實驗者常因時間、人力和成本的考量而無法取得完整的樣本資料，這類型的不完整資料稱為設限樣本。近年來有許多不同類型的設限方法發展出來，而逐步型Ⅱ設限即是其中的一種。
　　在本文中我們所要探討的主題就是在逐步型Ⅱ設限與一般化逐步型Ⅱ設限的方法下所獲得之有序樣本經過適當的轉換，可得到一組來自標準指數分配的樣本。接著利用此組樣本建構一些新的樞紐量，分別對Gompertz分配與極值分配進行假設檢定與信賴區間之推論，並以模擬結果來比較所有方法的表現優劣，找出最佳的方法。最後以數值實例來示範本論文提出的所有方法。

關鍵字

逐步型Ⅱ設限 ； 一般化逐步型Ⅱ設限 ； Gompertz分配 ； 極值分配 ； 樞紐量 ； 信賴區間 ； 假設檢定 ； 概似比檢定

並列摘要

Due to the restriction of time, cost and material, experimenters often can not observe the complete data in the lifetime test. The incomplete data is called the censored sample. There are several types of censoring schemes developed in recent year and the progressive type Ⅱ censoring scheme is one of those.
　By using a transformation, the progressive type Ⅱ censored sample and the general progressive type Ⅱ censored sample from the Gompertz distribution and the Extreme-Value distribution will become the progressive type Ⅱ censored sample and the general progressive type Ⅱ censored sample from the standard exponential distribution. In this paper, we proposed some new pivotal quantities to do the interval estimations and the hypothesis testing for the Gompertz distribution and the Extreme-Value distribution. We do a simulation to compare the performances of all methods in this paper. At last, one numerical example is given to demonstrate all proposed methods.

並列關鍵字

Confidence interval ； General progressive type Ⅱ censoring ； Hypothesis testing ； Pivotal quantity ； Progressive type Ⅱ censoring

參考文獻

[2] 廖佩怡(民95), 一般化型二逐步設限下對雙參數Gompertz分配

[13] Wu, J. W., Lu, L. H., Chen, C. H. and Wu. C. H.

[1] Balakrishnan, N. and Aggarwala, R. (2000),

Progressive Censoring Theory, Methods and

Applications, Birkhauser, Boston.