System No.  U00020602201023222600 

Title (in Chinese)  對極端母體的同時推論和在異質性下選出所有好母體的程序之研究 
Title (in English)  A study on the simultaneous confidence intervals for all distances from the extreme populations and the procedure of selecting all good populations under heteroscedasticity 
Other Title  
Institution  淡江大學 
Department (in Chinese)  管理科學研究所博士班 
Department (in English)  Graduate Institute of Management Science 
Other Division  
Other Division Name  
Other Department/Institution  
Academic Year  98 
Semester  1 
PublicationYear  99 
Author's name (in Chinese)  余玉如 
Author's name(in English)  YuhRu Yu 
Student ID  894560605 
Degree  博士 
Language  English 
Other Language  
Date of Oral Defense  20100108 
Pagination  156page 
Committee Member 
advisor

ShuFei Wu
cochair  JongWuu Wu cochair  YiTing Hwang cochair  WenChuan Lee cochair  ChihLi Wang cochair  LiangYu Ouyang cochair  ChinChuan Wu 
Keyword (inChinese) 
多重型II設限 單階段程序 正確選擇機率 同時推論 子集選擇 雙階段程序 
Keyword (in English) 
Multiply type II censoring Onestage procedure Probability of correct selection Simultaneous inference Subset selection Twostage procedure 
Other Keywords  
Subject  
Abstract (in Chinese) 
本論文之內容主要包含「對極端母體的同時推論」和「在異質性下選出所有好母體的程序」兩個主題。在第一個研究主題中，我們考慮k個獨立雙參數指數母體，具有未知的位置參數與共同且未知的尺度參數，在多重型II設限樣本下，利用14種估計量建立14個位置參數與極端母體距離及位置參數與最高極端母體距離之同時信賴區間，並且使用蒙地卡羅模擬法來模擬出臨界值。以最小信賴區間長度為衡量區間估計量表現好壞的準則，考慮在不同的設限組合之下，我們從14種同時信賴區間中選出最好的。文中也提出同時選擇極端母體之子集選擇程序，並舉出兩個數值例子作為極端母體同時推論與子集選擇程序之示範。在第二個研究主題中，考慮k個獨立常態母體，當母體變異數未知且可能不相等時，我們提出設計導向的雙階段程序選出所有好母體，並且證明正確選擇的機率P能夠高出原先設定的機率值P*。然而這種雙階段抽樣程序在第二階段時所需要的額外樣本，有可能因為預算的限制、計畫被終止或是其他的原因而導致無法取得，使得在做統計分析時，只有一組樣本可用，因此我們也提出資料分析的單階段程序選出所有好母體，並且舉一個實例來說明雙階段程序與單階段程序方法之應用。 
Abstract (in English) 
This thesis focuses on two topics: the simultaneous confidence intervals (SCIs) for all distances from the extreme populations (the lower extreme population (LEP) and the upper extreme population (UEP)) and the procedure of selecting all good populations under heteroscedasticity. Firstly, 14 SCIs for all distances from the extreme populations and from the UEP for k independent twoparameter exponential populations with unknown location parameters and common unknown scale parameter based on the multiply type II censored samples are proposed. The critical values are obtained by the MonteCarlo method. The optimal SCIs among 14 methods are identified based on the criteria of minimum confidence length for various censoring schemes. The subset selection procedures of extreme populations are also proposed and two numerical examples are given for illustration. Secondly, suppose that k independent normal populations with means Mu_1,Mu_2,...,Mu_k and variances Sigmasquare_1,Sigmasquare_2,...,Sigmasquare_k are considered. When variances are unknown and possibly unequal, a designoriented twostage procedure selecting all good populations such that the probability of correct selection P being greater than a prespecified value of P* is proposed. When the additional samples at the second stage may not be available due to the experimental budget shortage or other factors in an experiment, a dataanalysis onestage procedure selecting all good populations is proposed. One reallife example is given to illustrate all procedures. 
Other Abstract  
Table of Content (with Page Number) 
Contents Abstract in Chinese.....I Abstract in English.....II Contents.....III List of Tables.....V List of Figures.....VIII List of Notations.....IX Chapter 1 Introduction.....1 1.1 The SCIs for all distances from the extreme populations for twoparameter exponential populations.....1 1.2 A procedure of selecting all good populations for normal populations.....3 1.3 Organization of this dissertation.....4 Chapter 2 The SCIs for all distances from the extreme populations for twoparameter exponential populations.....6 2.1 The SCIs for all distances from the LEP and UEP.....7 2.2 Simulation comparisons.....15 2.3 Subset selection of extreme populations.....18 2.4 Numerical example.....19 2.5 Conclusions.....33 Chapter 3 A procedure of selecting all good populations for normal populations.....34 3.1 Twostage procedure.....34 3.2 Onestage procedure.....39 3.3 Controlling both types of errors.....42 3.4 Numerical example.....44 3.5 Simulation study.....51 3.6 Conclusions.....56 Chapter 4 Conclusions.....57 4.1 Conclusions for the SCIs for all distances from the extreme populations.....57 4.2 Conclusions for the procedure of selecting all good populations under heteroscedasticity.....58 References.....59 Appendix A Tables.....61 Appendix B Figures.....133 List of Tables Table 2.2.1 The recommended estimators with shorter confidence length than other estimators under various cases for twosided SCIs.....16 Table 2.2.2 The recommended estimators with shorter confidence length than other estimators under various cases for onesided SCIs.....17 Table 2.4.1 Simulated data for four populations.....20 Table 2.4.2 The required statistics.....21 Table 2.4.3 The 90% simultaneous confidence intervals.....22 Table 2.4.4 The 95% simultaneous confidence intervals.....23 Table 2.4.5 The 99% simultaneous confidence intervals.....24 Table 2.4.6 Results of subset selection for 1Alpha=0.90.....25 Table 2.4.7 Results of subset selection for 1Alpha=0.95.....25 Table 2.4.8 Results of subset selection for 1Alpha=0.99.....26 Table 2.4.9 Time intervals between failures.....27 Table 2.4.10 The required statistics.....28 Table 2.4.11 The 90% simultaneous confidence intervals.....29 Table 2.4.12 The 95% simultaneous confidence intervals.....30 Table 2.4.13 The 99% simultaneous confidence intervals.....31 Table 2.4.14 Results of subset selection for 1Alpha=0.90.....32 Table 2.4.15 Results of subset selection for 1Alpha=0.95.....32 Table 2.4.16 Results of subset selection for 1Alpha=0.99.....32 Table 3.1.1 Percentage points q*.....37 Table 3.4.1 Bacterial killing ability data.....44 Table 3.4.2 Immediate statistics of four solvents by the initial sample of size n0=14.....45 Table 3.4.3 Immediate statistics of four solvents for the twostage joint confidence interval.....45 Table 3.4.4 Subset of selected good populations for the twostage procedure.....45 Table 3.4.5 The 90% and 95% simultaneous inference of Mu_[4]Mu_i, i=1,2,3,4, for the twostage procedure.....46 Table 3.4.6 The 90% and 95% simultaneous inference of the ranked parameters for the twostage procedure.....47 Table 3.4.7 Immediate statistics of four solvents for the singlestage joint confidence interval.....48 Table 3.4.8 Subset of selected good populations for the onestage procedure.....48 Table 3.4.9 The 90% and 95% simultaneous inference of Mu_[4]Mu_i, i=1,2,3,4, for the onestage procedure.....49 Table 3.4.10 The 90% and 95% simultaneous inference of the ranked parameters for the onestage procedure.....50 Table 3.5.1 The simulation results for P*=0.90.....54 Table 3.5.2 The simulation results for P*=0.95.....55 Table A.1 The critical values of dt for the 90% SCIs for all distances from the LEP and UEP under equal censoring schemes.....61 Table A.2 The critical values of dt for the 95% SCIs for all distances from the LEP and UEP under equal censoring schemes.....66 Table A.3 The critical values of dt for the 99% SCIs for all distances from the LEP and UEP under equal censoring schemes.....71 Table A.4 The critical values of dt for the 90% SCIs for all distances from the UEP under equal censoring schemes.....76 Table A.5 The critical values of dt for the 95% SCIs for all distances from the UEP under equal censoring schemes.....81 Table A.6 The critical values of dt for the 99% SCIs for all distances from the UEP under equal censoring schemes.....86 Table A.7 The critical values of dt for the 90% SCIs for all distances from the LEP and UEP under unequal censoring schemes when k=4.....91 Table A.8 The critical values of dt for the 95% SCIs for all distances from the LEP and UEP under unequal censoring schemes when k=4.....92 Table A.9 The critical values of dt for the 99% SCIs for all distances from the LEP and UEP under unequal censoring schemes when k=4.....93 Table A.10 The critical values of dt for the 90% SCIs for all distances from the UEP under unequal censoring schemes when k=4.....94 Table A.11 The critical values of dt for the 95% SCIs for all distances from the UEP under unequal censoring schemes when k=4.....95 Table A.12 The critical values of dt for the 99% SCIs for all distances from the UEP under unequal censoring schemes when k=4.....96 Table A.13 The values of dt*Theta_t_hat_star/n for the 90% SCIs for all distances from the LEP and UEP under equal censoring schemes.....97 Table A.14 The values of dt*Theta_t_hat_star/n for the 95% SCIs for all distances from the LEP and UEP under equal censoring schemes.....102 Table A.15 The values of dt*Theta_t_hat_star/n for the 99% SCIs for all distances from the LEP and UEP under equal censoring schemes.....107 Table A.16 The values of dt*Theta_t_hat_star/n for the 90% SCIs for all distances from the UEP under equal censoring schemes.....112 Table A.17 The values of dt*Theta_t_hat_star/n for the 95% SCIs for all distances from the UEP under equal censoring schemes.....117 Table A.18 The values of dt*Theta_t_hat_star/n for the 99% SCIs for all distances from the UEP under equal censoring schemes.....122 Table A.19 The values of dt*Theta_t_hat_star/n for the 90% SCIs for all distances from the LEP and UEP under unequal censoring schemes when k=4.....127 Table A.20 The values of dt*Theta_t_hat_star/n for the 95% SCIs for all distances from the LEP and UEP under unequal censoring schemes when k=4.....128 Table A.21 The values of dt*Theta_t_hat_star/n for the 99% SCIs for all distances from the LEP and UEP under unequal censoring schemes when k=4.....129 Table A.22 The values of dt*Theta_t_hat_star/n for the 90% SCIs for all distances from the UEP under unequal censoring schemes when k=4.....130 Table A.23 The values of dt*Theta_t_hat_star/n for the 95% SCIs for all distances from the UEP under unequal censoring schemes when k=4.....131 Table A.24 The values of dt*Theta_t_hat_star/n for the 99% SCIs for all distances from the UEP under unequal censoring schemes when k=4.....132 List of Figures Figure 1.1.1 The multiply type II censoring.....2 Figure 3.4.1 The 90% and 95% simultaneous inference of Mu_[4]Mu_i, i=1,2,3,4, for the twostage procedure.....46 Figure 3.4.2 The 90% and 95% simultaneous inference of the ranked parameters for the twostage procedure.....47 Figure 3.4.3 The 90% and 95% simultaneous inference of Mu_[4]Mu_i, i=1,2,3,4, for the onestage procedure.....49 Figure 3.4.4 The 90% and 95% simultaneous inference of the ranked parameters for the onestage procedure.....50 Figure B.1 The critical values of dt for the 90% SCIs for all distances from the LEP and UEP for 14 estimators under various censoring schemes.....133 Figure B.2 The critical values of dt for the 95% SCIs for all distances from the LEP and UEP for 14 estimators under various censoring schemes.....135 Figure B.3 The critical values of dt for the 99% SCIs for all distances from the LEP and UEP for 14 estimators under various censoring schemes.....137 Figure B.4 The critical values of dt for the 90% SCIs for all distances from the UEP for 14 estimators under various censoring schemes.....139 Figure B.5 The critical values of dt for the 95% SCIs for all distances from the UEP for 14 estimators under various censoring schemes.....141 Figure B.6 The critical values of dt for the 99% SCIs for all distances from the UEP for 14 estimators under various censoring schemes.....143 Figure B.7 The values of dt*Theta_t_hat_star/n for the 90% SCIs for all distances from the LEP and UEP for 14 estimators under various censoring schemes.....145 Figure B.8 The values of dt*Theta_t_hat_star/n for the 95% SCIs for all distances from the LEP and UEP for 14 estimators under various censoring schemes.....147 Figure B.9 The values of dt*Theta_t_hat_star/n for the 99% SCIs for all distances from the LEP and UEP for 14 estimators under various censoring schemes.....149 Figure B.10 The values of dt*Theta_t_hat_star/n for the 90% SCIs for all distances from the UEP for 14 estimators under various censoring schemes.....151 Figure B.11 The values of dt*Theta_t_hat_star/n for the 95% SCIs for all distances from the UEP for 14 estimators under various censoring schemes.....153 Figure B.12 The values of dt*Theta_t_hat_star/n for the 99% SCIs for all distances from the UEP for 14 estimators under various censoring schemes.....155 
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