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中文論文名稱 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
英文論文名稱 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
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 95
學期 2
出版年 96
研究生中文姓名 蘇均哲
研究生英文姓名 Chun-Che Su
學號 694460212
學位類別 碩士
語文別 中文
口試日期 2007-06-05
論文頁數 248頁
口試委員 指導教授-吳淑妃
委員-王智立
委員-吳錦全
中文關鍵字 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 
英文關鍵字 Confidence interval  General progressive type Ⅱ censoring  Hypothesis testing  Pivotal quantity  Progressive type Ⅱ censoring 
學科別分類 學科別自然科學統計
中文摘要   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。
英文摘要  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.
論文目次 第一章 緒論..1
1.1前言..1
1.2研究動機與目的..1
1.3本文架構..4
第二章 文獻探討..5
2.1逐步型Ⅱ設限之相關文獻探討..5
2.2推論方法之相關文獻探討..5
第三章 Gompertz分配在逐步型Ⅱ設限與一般化逐步型Ⅱ設限樣本下
之統計推論..8
3.1前言..8
3.2在逐步型Ⅱ設限與一般化逐步型Ⅱ設限下Gompertz分配模型的建
立與樞紐量之建構..9
3.2.1 逐步型Ⅱ設限樣本下樞紐量之建立..11
3.2.2 一般化逐步型Ⅱ設限樣本下樞紐量之建立..16
3.3 形狀參數β之信賴區間的建立..24
3.3.1 在逐步型Ⅱ設限下對形狀參數 的區間估計..24
3.3.2在一般化逐步型Ⅱ設限下對形狀參數 的區間估計..25
3.4 形狀參數β之假設檢定..27
3.4.1 逐步型Ⅱ設限下形狀參數β之假設檢定..27
3.4.2 一般化逐步型Ⅱ設限下形狀參數β之假設檢定..30
3.5 數值模擬比較..34
3.5.1 Gompertz分配之逐步型Ⅱ設限與一般化逐步型Ⅱ設限樣本之
模擬方法與樞紐量百分位數模擬方法..34
3.5.2 信賴區間之模擬..37
3.5.3 假設檢定檢定力之模擬..41
3.6 數值實例..61
第四章 極值分配在逐步型Ⅱ設限與一般化逐步型Ⅱ設限樣本下之統計推論..65
4.1前言..65
4.2在逐步型Ⅱ設限與一般化逐步型Ⅱ設限下極值分配模型的建立與樞紐量之建構..66
4.2.1 逐步型Ⅱ設限樣本下樞紐量之建立..68
4.2.2 一般化逐步型Ⅱ設限樣本下樞紐量之建立..74
4.3 尺度參數θ信賴區間之建立..82
4.3.1 在逐步型Ⅱ設限下對尺度參數θ的區間估計..82
4.3.2在一般化逐步型Ⅱ設限下對尺度參數θ的區間估計..83
4.4 尺度參數θ之假設檢定..84
4.4.1 逐步型Ⅱ設限下尺度參數θ之假設檢定..85
4.4.2 一般化逐步型Ⅱ設限下尺度參數θ之假設檢定..88
4.5 數值模擬比較..92
4.5.1極值分配之逐步型Ⅱ設限與一般化逐步型Ⅱ設限樣本模擬方
法..92
4.5.2 信賴區間之模擬..95
4.5.3 假設檢定檢定力之模擬..98
4.6數值實例..118
第五章 結論..122
參考文獻..124
附錄..127

圖目錄
圖3.1:Gompertz 分配之機率密度函數圖.............................................9
圖3.2:Gompertz 分配之故障率函數圖...............................................10
圖3.3: n = 10、m = 8 、r = 0、顯著水準α = 0.05之下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較圖.......................44
圖3.4:n = 10、m = 8、r = 1、顯著水準α = 0.05之下,固定設限下各樞
紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較圖...........................45
圖3.5: n = 10、m = 8 、r = 2 、顯著水準α = 0.05之下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較圖.......................46
圖3.6:n = 20 、m = 18 、r = 0、顯著水準α = 0.05之下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較圖.......................47
圖3.7: n = 20 、m = 18 、r = 1、顯著水準α = 0.05之下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較圖.......................48
圖3.8:n = 20 、m = 18 、r = 2 、顯著水準α = 0.05之下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較圖.......................49
圖3.9:n = 45、m = 40、r = 0、顯著水準α = 0.05之下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖....52
圖3.10:n = 45、m = 40、r = 1顯著水準α = 0.05之下,固定設限下各樞
紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖........53

圖3.11: n = 45、m = 40、r = 2 、顯著水準α = 0.05之下,固定設限下
各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖.54
圖3.12: n = 65、m = 60 、r = 0、顯著水準α = 0.05之下,固定設限下
各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖55
圖3.13:n = 65、m = 60、r = 1、顯著水準α = 0.05之下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖....56
圖3.14: n = 65、m = 60 、r = 2 、顯著水準α = 0.05之下,固定設限下
各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖57
圖3.15:n = 125、m = 120、r = 0、顯著水準α = 0.05下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖....58
圖3.16:n = 125、m = 120 、r = 1、顯著水準α = 0.05下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖....59
圖3.17:n = 125、m = 120、r = 2 、顯著水準α = 0.05下,固定設限下各
樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比較圖....60
圖4.1:極值分配之機率密度函數圖....................................................66
圖4.2:極值分配之故障率函數圖........................................................67
圖4.3: n = 10、m = 8 、r = 0 、β = 1、顯著水準α = 0.05之下,固定設
限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較圖...........101

圖4.4: n = 10、m = 8 、r = 1、β = 1、顯著水準α = 0.05之下,固定設
限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較圖...........102
圖4.5: n = 10、m = 8 、r = 2 、β = 1、顯著水準α = 0.05之下,固定設
限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較圖...........103
圖4.6:n = 20 、m = 18、r = 0 、β = 1、顯著水準α = 0.05之下,固定設
限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較圖...........104
圖4.7:n = 20 、m = 18 、r = 1、β = 1、顯著水準α = 0.05之下,固定設
限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較圖...........105
圖4.8:n = 20 、m = 18、r = 2、β = 1、顯著水準α = 0.05之下,固定設
限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較圖...........106
圖4.9:n = 45、m = 40、r = 0 、β = 1、顯著水準α = 0.05之下,固定設
限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比較
圖.........................................................................................................109
圖4.10: n = 45、m = 40、r = 1、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................110
圖4.11: n = 45、m = 40、r = 2 、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................111

圖4.12: n = 65、m = 60 、r = 0 、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................112
圖4.13: n = 65、m = 60 、r = 1、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................113
圖4.14: n = 65、m = 60 、r = 2 、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................114
圖4.15:n = 125、m = 120、r = 0 、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................115
圖4.16:n = 125、m = 120、r = 1、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................116
圖4.17:n = 125、m = 120、r = 2、β = 1、顯著水準α = 0.05之下,固定
設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 與LR 檢定之檢定力比
較圖.....................................................................................................117

附錄
附錄1:設限計劃表.............................................................................150
附表1.1:小樣本設限計劃表.......................................................150
附表1.1(續):小樣本設限計劃表.................................................151
附表1.2 :大樣本設限計劃表.....................................................151
附錄2:樞紐量百分位數表.................................................................152
附表2.1: n = 10,m = 6 , r = 0 樞紐量百分位數表.....................152
附表2.2: n = 10,m = 7 , r = 0 樞紐量百分位數表.....................152
附表2.3: n = 10,m = 8 , r = 0 樞紐量百分位數表.....................152
附表2.4: n = 10,m = 9 , r = 0 樞紐量百分位數表.....................153
附表2.5: n = 10,m = 10 ,r = 0 樞紐量百分位數表....................153
附表2.6: n = 10,m = 6 , r = 1樞紐量百分位數表......................153
附表2.7: n = 10,m = 7 , r = 1樞紐量百分位數表......................154
附表2.7(續): n = 10,m = 7 , r = 1樞紐量百分位數表...............154
附表2.8: n = 10,m = 8 , r = 1樞紐量百分位數表......................154
附表2.8(續): n = 10,m = 8 , r = 1樞紐量百分位數表...............155
附表2.9: n = 10,m = 9 , r = 1樞紐量百分位數表......................155
附表2.10: n = 10,m = 10 , r = 1樞紐量百分位數表..................155
附表2.11: n = 10,m = 6 ,r = 2 樞紐量百分位數表...................156

附表2.12: n = 10,m = 7 , r = 2 樞紐量百分位數表...................156
附表2.12(續): n = 10,m = 7 , r = 2 樞紐量百分位數表............157
附表2.13: n = 10,m = 8 , r = 2 樞紐量百分位數表...................157
附表2.14: n = 10,m = 9 , r = 2 樞紐量百分位數表...................157
附表2.14(續): n = 10,m = 9 , r = 2 樞紐量百分位數表............158
附表2.15: n = 10,m = 10 , r = 2 樞紐量百分位數表..................158
附表2.16: n = 20 ,m = 16 , r = 0 樞紐量百分位數表.................158
附表2.17: n = 20 ,m = 17 , r = 0 樞紐量百分位數表.................159
附表2.18: n = 20 ,m = 18 , r = 0 樞紐量百分位數表.................159
附表2.19: n = 20 ,m = 19 , r = 0 樞紐量百分位數表.................159
附表2.20: n = 20 ,m = 20, r = 0 樞紐量百分位數表.................160
附表2.21: n = 20 ,m = 16 , r = 1樞紐量百分位數表..................160
附表2.22: n = 20 ,m = 17 , r = 1樞紐量百分位數表..................160
附表2.22(續): n = 20 ,m = 17 , r = 1樞紐量百分位數表...........161
附表2.23: n = 20 ,m = 18 , r = 1樞紐量百分位數表..................161
附表2.24: n = 20 ,m = 19 , r = 1樞紐量百分位數表..................162
附表2.25: n = 20 ,m = 20, r = 1樞紐量百分位數表.................162
附表2.26: n = 20 ,m = 16 , r = 2 樞紐量百分位數表.................162
附表2.26(續): n = 20 ,m = 16 , r = 2 樞紐量百分位數表..........163

附表2.27: n = 20 ,m = 17 , r = 2 樞紐量百分位數表.................163
附表2.28: n = 20 ,m = 18 , r = 2 樞紐量百分位數表.................164
附表2.29: n = 20 ,m = 19 , r = 2 樞紐量百分位數表.................164
附表2.29(續): n = 20 ,m = 19 , r = 2 樞紐量百分位數表..........165
附表2.30: n = 20 ,m = 20, r = 2 樞紐量百分位數表.................165
附表2.31: n = 45,m = 40 ,r = 0 樞紐量百分位數表.................166
附表2.32: n = 65,m = 60 ,r = 0 樞紐量百分位數表.................166
附表2.33: n = 125,m = 120 , r = 0 樞紐量百分位數表..............166
附表2.34: n = 45,m = 40 , r = 1樞紐量百分位數表..................167
附表2.35: n = 65,m = 60 , r = 1樞紐量百分位數表..................167
附表2.35(續): n = 65,m = 60 , r = 1樞紐量百分位數表...........168
附表2.36: n = 125,m = 120 , r = 1樞紐量百分位數表...............168
附表2.37: n = 45,m = 40 ,r = 2 樞紐量百分位數表.................168
附表2.37(續): n = 45,m = 40, r = 2 樞紐量百分位數表..........169
附表2.38: n = 65,m = 60 ,r = 2 樞紐量百分位數表.................169
附表2.39: n = 125,m = 120 , r = 2 樞紐量百分位數表.................170
附錄3:Gompertz 分配形狀參數β 信賴區間模擬結果.....................171
附表3.1:n = 10、β = 0.01、λ = 0.01、r = 0、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表................171

附表3.2:n = 10、β = 0.01、λ = 0.01、r = 1、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................172
附表3.3:n = 10、β = 0.01、λ = 0.01、r = 2、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................173
附表3.4:n = 20、β = 0.01、λ = 0.01、r = 0、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................174
附表3.5:n = 20、β = 0.01、λ = 0.01、r = 1、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................175
附表3.6:n = 20、β = 0.01、λ = 0.01、r = 2、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................176
附表3.7:n = 10、β = 0.01、λ = 0.01、r = 0、信心水準1−α = 0.95之
下,固定設限下各樞紐量h 的平均區間長度比較表..............177
附表3.8:n = 10、β = 0.01、λ = 0.01、r = 1、信心水準1−α = 0.95之
下,固定設限下各樞紐量h 的平均區間長度比較表..............178
附表3.9:n = 10、β = 0.01、λ = 0.01、r = 2、信心水準1−α = 0.95之
下,固定設限下各樞紐量h 的平均區間長度比較表..............179
附表3.10:n = 20 、β = 0.01、λ = 0.01、r = 0 、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........180
131
附表3.10(續):n = 20、β = 0.01、λ = 0.01、r = 0、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........181
附表3.10(續):n = 20、β = 0.01、λ = 0.01、r = 0、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........182
附表3.11: n = 20 、β = 0.01、λ = 0.01、r = 1、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........183
附表3.11(續):n = 20、β = 0.01、λ = 0.01、r = 1、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........184
附表3.11(續):n = 20、β = 0.01、λ = 0.01、r = 1、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........185
附表3.12:n = 20 、β = 0.01、λ = 0.01、r = 2、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........186
附表3.12(續):n = 20、β = 0.01、λ = 0.01、r = 2、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........187
附表3.12(續):n = 20、β = 0.01、λ = 0.01、r = 2、信心水準1−α = 0.95
之下, 固定設限下各樞紐量h 的平均區間長度比較表...........188

附錄4:Gompertz 分配形狀參數β 小樣本假設檢定模擬結果.........189
附表4.1: n = 10、m = 6 、λ = 0.1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................189
附表4.2: n = 10、m = 7 、λ = 0.1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................189
附表4.3: n = 10、m = 8 、λ = 0.1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................189
附表4.4: n = 10、m = 9 、λ = 0.1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................190
附表4.5:n = 10、m = 10、λ = 0.1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................190
附表4.6: n = 10、m = 6 、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................190

附表4.6(續): n = 10、m = 6 、λ = 0.1、r = 1、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................191
附表4.7: n = 10、m = 7 、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................191
附表4.8: n = 10、m = 8 、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................192
附表4.9: n = 10、m = 9 、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................192
附表4.9(續): n = 10、m = 9 、λ = 0.1、r = 1、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................193
附表4.11:n = 10、m = 6、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................193

附表4.11(續):n = 10、m = 6、λ = 0.1、r = 2、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................194
附表4.12:n = 10、m = 7、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................194
附表4.13:n = 10、m = 8、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................195
附表4.14:n = 10、m = 9、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................195
附表4.14(續):n = 10、m = 9、λ = 0.1、r = 2、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................196
附表4.15:n = 10、m = 10、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................196

附表4.16:n = 20、m = 16、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................196
附表4.17:n = 20、m = 17、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................197
附表4.18:n = 20、m = 18、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................197
附表4.19:n = 20、m = 19、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................197
附表4.20:n = 20、m = 20、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................198
附表4.21:n = 20、m = 16、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................198

附表4.22:n = 20、m = 17、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................198
附表4.22(續):n = 20、m = 17、λ = 0.1、r = 1、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................199
附表4.23:n = 20、m = 18、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................199
附表4.24:n = 20、m = 19、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................200
附表4.25:n = 20、m = 20、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................200
附表4.26:n = 20、m = 16、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................201

附表4.27:n = 20、m = 17、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................201
附表4.27(續):n = 20、m = 17、λ = 0.1、r = 2、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................202
附表4.28:n = 20、m = 18、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................202
附表4.29:n = 20、m = 19、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................203
附表4.30:n = 20、m = 20、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................203
附錄5:Gompertz 分配形狀參數β 大樣本假設檢定模擬結果.........204
附表5.1:n = 45、m = 40、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................204

附表5.2:n = 65、m = 60、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................204
附表5.3:n = 125、m = 120、λ = 0.1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................204
附表5.4:n = 45、m = 40、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................205
附表5.5:n = 65、m = 60、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................205
附表5.5(續):n = 65、m = 60 、λ = 0.1、r = 1、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................206
附表5.6:n = 125、m = 120、λ = 0.1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................206

附表5.7:n = 45、m = 40、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................207
附表5.8:n = 65、m = 60、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................207
附表5.8(續):n = 65、m = 60、λ = 0.1、r = 2、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力
比較表..........................................................................................208
附表5.9:n = 125、m = 120、λ = 0.1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較
表..................................................................................................208
附表5.10:λ = 0.1、r = 0 、顯著水準α = 0.05之下,固定設限下概
似比檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較表...................209
附表5.11:λ = 0.1、r = 1、顯著水準α = 0.05之下,固定設限下概
似比檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較表...................209
附表5.13:λ = 0.1、r = 2 、顯著水準α = 0.05之下,固定設限下概
似比檢定: 1 0 H β = v.s. : 1 1 H β ≠ 之檢定力比較表...................209

附錄6:極值分配尺度參數θ 信賴區間模擬結果..............................210
附表6.1:n = 10、β = 0.01、θ = 0.01、r = 0、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................210
附表6.2:n = 10、β = 0.01、θ = 0.01、r = 1、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................211
附表6.3:n = 10、β = 0.01、θ = 0.01、r = 2、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................212
附表6.4:n = 20、β = 0.01、θ = 0.01、r = 0、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................213
附表6.5:n = 20、β = 0.01、θ = 0.01、r = 1、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................214
附表6.6:n = 20、β = 0.01、θ = 0.01、r = 2、信心水準1−α = 0.95之
下,固定設限下各樞紐量的平均區間長度比較表.................215
附表6.7:n = 10、β = 0.01、θ = 0.01、r = 0、信心水準1−α = 0.95之
下,固定設限下各樞紐量h 的平均區間長度比較表..............216
附表6.8:n = 10、β = 0.01、θ = 0.01、r = 1、信心水準1−α = 0.95之
下,固定設限下各樞紐量h 的平均區間長度比較表..............217
附表6.9:n = 10、β = 0.01、θ = 0.01、r = 2、信心水準1−α = 0.95之
下,固定設限下各樞紐量h 的平均區間長度比較表..............218

附表6.10:n = 20 、β = 0.01、θ = 0.01、r = 0 、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........219
附表6.10(續):n = 20、β = 0.01、θ = 0.01、r = 0、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........220
附表6.10(續):n = 20、β = 0.01、θ = 0.01、r = 0、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........221
附表6.11:n = 20、β = 0.01、θ = 0.01、r = 1、信心水準1−α = 0.95之
下,固定設限下各樞紐量h 的平均區間長度比較表..............222
附表6.11(續):n = 20、β = 0.01、θ = 0.01、r = 1、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........223
附表6.11(續):n = 20、β = 0.01、θ = 0.01、r = 1、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........224
附表6.12:n = 20 、β = 0.01、θ = 0.01、r = 2 、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........225
附表6.12(續):n = 20、β = 0.01、θ = 0.01、r = 2、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........226
附表6.12(續):n = 20、β = 0.01、θ = 0.01、r = 2、信心水準1−α = 0.95
之下,固定設限下各樞紐量h 的平均區間長度比較表..........227

附錄7:極值分配尺度參數θ 小樣本假設檢定模擬結果..................228
附表7.1:n = 10、m = 6、β = 1、r = 0、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................228
附表7.2:n = 10、m = 7、β = 1、r = 0、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................228
附表7.3:n = 10、m = 8、β = 1、r = 0、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................228
附表7.4:n = 10、m = 9、β = 1、r = 0、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................229
附表7.5: n = 10、m = 10 、β = 1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................229
附表7.6:n = 10、m = 6、β = 1、r = 1、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................229
附表7.6(續):n = 10、m = 6、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................230

附表7.7:n = 10、m = 7、β = 1、r = 1、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................230
附表7.8:n = 10、m = 8 、β = 1、r = 1、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................231
附表7.9:n = 10、m = 9、β = 1、r = 1、顯著水準α = 0.05之下,固
定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表
......................................................................................................231
附表7.9(續):n = 10、m = 9、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................232
附表7.10: n = 10、m = 10 、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................232
附表7.11: n = 10、m = 6 、β = 1、r = 2 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................232
附表7.11(續): n = 10、m = 6 、β = 1、r = 2 、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比
較表..............................................................................................233

附表7.12: n = 10、m = 7 、β = 1、r = 2 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................233
附表7.13: n = 10、m = 8 、β = 1、r = 2 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................234
附表7.14: n = 10、m = 9 、β = 1、r = 2 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................234
附表7.14(續): n = 10、m = 9 、β = 1、r = 2 、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比
較表..............................................................................................235
附表7.15:n = 10、m = 10、β = 1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................235
附表7.16:n = 20 、m = 16、β = 1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................235

附表7.17:n = 20 、m = 17、β = 1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................236
附表7.18:n = 20 、m = 18、β = 1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................236
附表7.19:n = 20 、m = 19、β = 1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................236
附表7.20:n = 20、m = 20、β = 1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................237
附表7.21:n = 20 、m = 16、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................237
附表7.22:n = 20 、m = 17、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................237

附表7.22(續): n = 20 、m = 17 、β = 1、r = 1、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比
較表..............................................................................................238
附表7.23:n = 20 、m = 18、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................238
附表7.24:n = 20 、m = 19、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................239
附表7.25:n = 20 、m = 20、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................239
附表7.26:n = 20 、m = 16、β = 1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................240
附表7.27:n = 20 、m = 17、β = 1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................240

附表7.27(續):n = 20 、m = 17 、β = 1、r = 2 、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比
較表..............................................................................................241
附表7.28:n = 20 、m = 18、β = 1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................241
附表7.29:n = 20 、m = 19、β = 1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................242
附表7.30:n = 20、m = 20、β = 1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................242
附錄8:極值分配尺度參數θ 大樣本假設檢定模擬結果..................243
附表8.1: n = 45、m = 40、β = 1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................243
附表8.2: n = 65、m = 60 、β = 1、r = 0 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................243

附表8.3:n = 125、m = 120、β = 1、r = 0、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................243
附表8.4: n = 45、m = 40、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................244
附表8.5: n = 65、m = 60 、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................244
附表8.5(續):n = 65、m = 60、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................245
附表8.6:n = 125、m = 120、β = 1、r = 1、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................245
附表8.7: n = 45、m = 40、β = 1、r = 2 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................246

附表8.8: n = 65、m = 60 、β = 1、r = 2 、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................246
附表8.8(續): n = 65、m = 60 、β = 1、r = 2 、顯著水準α = 0.05之
下,固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比
較表..............................................................................................247
附表8.9:n = 125、m = 120、β = 1、r = 2、顯著水準α = 0.05之下,
固定設限下各樞紐量檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較
表..................................................................................................247
附表8.10:β = 1、r = 0、顯著水準α = 0.05之下,固定設限下概似
比檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表........................248
附表8.11:β = 1、r = 1、顯著水準α = 0.05之下,固定設限下概似
比檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表........................248
附表8.12:β = 1、r = 2、顯著水準α = 0.05之下,固定設限下概似
比檢定: 1 0 H θ = v.s. : 1 1 H θ ≠ 之檢定力比較表........................248


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[1] 李百靈(民89), 以雙型II設限樣本探討Gompertz和極值分配之
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[2] 廖佩怡(民95), 一般化型二逐步設限下對雙參數Gompertz分配
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