在兩階段型II混合設限下指數分布的概似推論

Exact Likelihood Inference for the Exponential Distribution under two-stage Type-II Hybrid Censoring

林芝郁(Jy-Yuh Lin)

指導教授 ： 伍志祥

淡江大學/理學院/數學學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00165

摘要

設限資料的取樣方法分為基本型以及混合型兩種,會有觀測時間過長或是觀測到壽命的樣本個數太少的缺點.要改善觀測時間過長的缺點,需要設定一較短的觀測設限時間;要改善觀測到壽命的樣本個數太少的缺點,需要設定一最少觀測到壽命的樣本個數.這會產生兩難的情形.因此,在有最少觀測個數的限制下,本論文提出了兩階段取樣法,將取樣停止時間分為第一階段及第二階段,並設定一個判斷準則,在第一階段觀測時間結束時,用來決定是否進行第二階段的觀測.這不但可以得到足夠的樣本個數,而且也能改善觀測時間過長的缺點.
此外,本論文針對兩階段取樣法中的統計推論問題,作了一些探討.在隨機樣本的壽命為指數分布的假設下,研究參數之最大概似估計量、估計量之機率分配及信賴區間等問題,最後並用一實際例子來介紹本論文所討論的方法.

關鍵字

概似推論 ； 兩階段取樣法 ； 指數分布

並列摘要

The censoring schemes most commonly found in the literature are referred to as type-I, type-II and hybrid censoring. However, in these censoring schemes, there are some disadvantages which are that have a few number of failures or take a very long time for observing the expected number of failure in the life test. For determining the censoring time, we must to meet one of these two situations. In order to provide a guarantee in terms of the number of failures as well as saving the time to complete the life test. We propose two-stage hybrid censoring schemes. That is given two censoring time and one constrain for determine which one is the true censoring time in the life test.
In addition, we also derive the exact distribution of the MLE of Θ as well as exact confidence intervals for Θ of the exponential distribution under two-stage hybrid censoring schemes. Finally, one sample is presented to illustrate all the results developed here.

並列關鍵字

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

參考文獻

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