A study on the simultaneous confidence intervals for all distances from the extreme populations and the procedure of selecting all good populations under heteroscedasticity

• Main Authors: Yuh-Ru Yu, 余玉如
• Other Authors: Shu-Fei Wu
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/66304441360012652513

博士 === 淡江大學 === 管理科學研究所博士班 === 98 === 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 two-parameter 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 Monte-Carlo 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 Sigma-square_1,Sigma-square_2,...,Sigma-square_k are considered. When variances are unknown and possibly unequal, a design-oriented two-stage procedure selecting all good populations such that the probability of correct selection P being greater than a pre-specified 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 data-analysis one-stage procedure selecting all good populations is proposed. One real-life example is given to illustrate all procedures.