系統識別號 | U0002-2806200707242900 |
---|---|
DOI | 10.6846/TKU.2007.00909 |
論文名稱(中文) | 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 |
論文名稱(英文) | 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 |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 統計學系碩士班 |
系所名稱(英文) | Department of Statistics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 95 |
學期 | 2 |
出版年 | 96 |
研究生(中文) | 蘇均哲 |
研究生(英文) | Chun-Che Su |
學號 | 694460212 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2007-06-05 |
論文頁數 | 248頁 |
口試委員 |
指導教授
-
吳淑妃(100665@mail.tku.edu.tw)
委員 - 王智立 委員 - 吳錦全 |
關鍵字(中) |
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 |
關鍵字(英) |
Confidence interval General progressive type Ⅱ censoring Hypothesis testing Pivotal quantity Progressive type Ⅱ censoring |
第三語言關鍵字 | |
學科別分類 | |
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. |
第三語言摘要 | |
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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