兩階段混合型 M 設限下指數分配的概似估推論

Exact likelihood inference for the Exponential distribution under two-stage type M hybrid censoring.

王凰妃(Huang-Fei Wang)

指導教授 ： 伍志祥

淡江大學/理學院/數學學系碩士班/碩士(2006年)

https://doi.org/10.6846/TKU.2006.00924

摘要

設資料分為型I設限、 型II設限和混合型設限三種, 此三種取樣方式可能會面臨到觀測時間過長或是觀測到的樣本數太少的問題, 若要改善觀測時間過長卻觀察到太少的樣本個數的問題,就必須設定最少的觀測個數; 若要改善觀測個數太少的問題,就必須設定一較長的觀測時間。 在此,我們在有最長觀測時間的限制下,提出兩階段型混合設限法, 將取樣時間分成兩個階段,在設定一個限制條件來判斷是否進行第二個階段, 這樣的設限方法,不僅可以解決所觀測到樣本各式過少的問題, 還可以縮短觀測的時間。本文在此兩階段混合設限的情況下, 討論當樣本壽命為指數分配時,其參數的最大概似估計量的分配、期望值、變異數及信賴區間等統計推論。

關鍵字

概似推論 ； 指數分布 ； 兩階段設限取樣

並列摘要

There are three sampleing methods of Type I、Type II and Mixing censoring for censoring data. However, such ways of sampling have some disadvantages which are that have few number of failures or take a long time for observating the expected number of failure in the life test. To prevent the defect of the shortcoming of samples under over-time, the observed sample must be extended. To improve the problem of the over-time of samples, the observed time must to fix a long time. In this paper, the end time of sampling period is divided into the first stage and second stage, and the criteria are set up for determining whether to procced to the second stage or not. So we could modify both of defect in the life test. Based on this two-staged sampling method, this paper further argues about the distribution, expection、 variance, and confidence interval of the estimation of the parameter under the distribution of the life time is exponential.

並列關鍵字

likelihood inference ； exponentional distribution ； two-stage hybrid censoring schemes

參考文獻

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