臺灣博碩士論文加值系統

在自然與工業界中，生物與產品的壽命往往是研究的重點，例如在醫學的臨床實驗中，有的病人在實驗未結束之前，可能因為某些因素而無法繼續實驗，又如在實驗中可能有一些實驗者對實驗有危險性，或不適合實驗的要求，而要提前結束實驗，為了解決這些問題，所以發展出數種設限與逐步移除的方法。本論文是探討二項與隨機移除型二逐步設限下
Rayleigh分配和Gompertz分配資料的統計分析。在文中，首先討論分配中參數的最大概似估計量與特性，並對隨機移除與二項移除兩方法分別探討，再推導Rayleigh分配與Gompertz分配在隨機與二項移除的期望時間，在分配的參數作一些變化計算出期望時間，再來加以分析Rayleigh分配與Gompertz分配在二項與隨機移除型二逐步設限下的期望時間。

Studies in the lifetimes of the organisms and products are often the main research topics in the nature and industries. The past research developed some censored methods. Before the experiments did not end yet, some patients might not proceed the experiments due to some factors. Furthermore, the experiments were ended early because some experimenters might be hazardous for the experiments during the experiments or not tally with the demands of the experiments. In order to resolve these problems, progressive removal was developed. This thesis mainly concentrates on the statistical analysis of Rayleigh distributed and Gompertz distributed life time data under Type II progressive censoring with binomial and random removals.
To begin with, the thesis discusses the maximum likelihood estimates andcharacteristics of the parameters in the distributions. We respectively narrate binomial and random removals. Then, we separately deduce the expected values of Rayleigh distribution and Gompertz distribution under binomial and random removals. Adjusting the parameter values of the distributions counts up to the expected time. Finally, we farther analyze the expected time of Rayleigh distribution and Gompertz distribution under Type II progressive censoring with binomial and random removals.

第一章 緒論………………………………………………………………….1
1-1前言………………………………………………………………1
1-2研究背景與動機………………………………………………2
1-3本文架構………………………………………………………5
第二章 文獻探討……………………………………………………………6
2-1 逐步設限之文獻探討…………………………………………6
2-2 型二逐步設限之文獻探討……………………………………6
2-3隨機與二項移除之型二逐步設限……………………………7
2-3-1隨機移除之型二逐步設限………………………………7
2-3-2二項移除之型二逐步設限………………………………9
第三章 Rayleigh分配之設限資料的統計分析……………………………11
3-1模式的建立……………………………………………………11
3-1-1二項移除之型二逐步設限………………………………12
3-1-2 隨機移除之型二逐步設限……………………………13
3-2 參數β與二項移除之機率p的估計………………………14
3-3 β的信賴區間……………………………………………….16
3-4 期望時間…………………………………………………….20
3-5 數值計算與分析…………………………………………….23
第四章 Gompertz分配之設限資料的統計分析……………………………25
4-1 模式的建立………………………………………………… 25
4-1-1 二項移除之型二逐步設限……………………………… 26
4-1-2 隨機移除之型二逐步設限………………………………27
4-2參數β、λ與二項移除之機率p的估計與特性……………27
4-2-1參數β、λ與二項移除之機率p的最大概似估計量…28
4-2-2參數β、λ的最大概似估計量之近似特性……………30
4-3 β與λ的信賴區間………………………………………….32
4-4 期望時間…………………………………………………….39
4-5 數值計算與分析…………………………………………….44
第五章 結論…………………………………………………………………46
圖表………………………………………………………………………….48
參考文獻…………………………………………………………………….65

一、中文部分
[1] 林尚賢(民89)，在第一失敗-設限抽樣方案下Weibull 分配和
Extreme-value 分配的參數估計，淡江大學統計學系應用統計所
碩士班碩士論文。
[2] 陳靜怡(民88)以截斷樣本探討指數分配及Rayleigh分配之尺度參數
的近似最大概似估計量，淡江大學統計學系應用統計所碩士班碩士論
文。
[3] 詹煌宇(民90)，二項與隨機移除之型二逐步設限下極值分配和柏
拉圖分配資料的統計分析，淡江大學統計學系應用統計所碩士班碩
士論文。
[4] 蔡志輝(民88)在第一失敗-設限抽樣方案下Gompertz分配的參數
估計，淡江大學統計學系應用統計所碩士班碩士論文。
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