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

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Multiply type II censoring ； One-stage procedure ； Probability of correct selection ； Simultaneous inference ； Subset selection ； Two-stage procedure

參考文獻

Balakrishnan, N., 1990, On the maximum likelihood estimation of the location and scale parameters of exponential distribution based on multiply type II censored samples. Journal of Applied Statistics, 17, 55-61.

Balasubramanian, K. and Balakrishnan, N., 1992, Estimation for one- and two-parameter exponential distributions under multiple type II censoring. Statistical Papers, 33, 203-216.

Bechhofer, R. E., 1954, A single-sample multiple decision procedure for ranking means of normal populations with known variances. The Annals of Mathematical Statistics, 25, 16-39.

Bishop, T. A. and Dudewicz, E. J., 1978, Exact analysis of variance with unequal variances: test procedures and tables. Technometrics, 20, 419-430.

Chen, H. J. and Lam, K., 1989, Single-stage interval estimation of the largest normal mean under heteroscedasticity. Communications in Statistics - Theory and Methods, 18(10), 3703-3718.

國際替代計量

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

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