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題 名 | Selecting the Smallest Normal Variance Through the Comparisons of Several Likelihoods |
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作 者 | 周文賢; | 書刊名 | 明志工專學報 |
卷 期 | 15 1983.06[民72.06] |
頁 次 | 頁1-26 |
分類號 | 319 |
關鍵詞 | |
語 文 | 英文(English) |
中文摘要 | 從K個常態母群體中,選出一個具有最小變異數的母群體。對這項統計方法,加以探討,是本篇論述的重點。本篇之研討,採用「無關區域帶趨近法」(indifference zone approach)。至於在選擇的正確機率方面,則希望能達到特定的機率值P*。下列作者之著作,可以作為查閱此類問題的重要參考資料:Bechhofer等(1968)、Gibbons等(1977)Gupta和panchapakesan(1979)。 此類問題可視為一種多重假設檢定(multiple-hypothesis testing)問題。本篇所建議順次檢定法,與一般習見的固定樣本法比較,在平均樣本的個數方面,有實質的「節省」。本篇採用二個不同的方法,去定義上述的所謂「節省」。至於在模擬的計算過程中,則僅使用其中的一個定義。 在母群體平均數全部或部分已知的特殊情況下,本篇也加以研究。在K=2對K=3時,由模擬所得的數據,可以看出本篇所建議的程序,確實有上述「節省」的優點。在K=2,當P*→1時,本篇將上述統計方法所涉及「停止時間」(stopping time)的各種趨近行為,加以研討,歸納於定理一與定理二當中。在K=3,當P*→1時,本篇將部分趨近結果,歸納於定理三當中。 |
英文摘要 | We are dealing with the problem of selecting the normal population having the smallest variance among k normal populations. We adopt the “indifference zone approach” with a target value of the probability of correct selection P*. One may refer to Bechhofer et al (1968), Gibbons et al (1977) and Gupta and Pancha-pakeasn (1979). We view this problem as a multiple-hypothesis testing problem and we propose sequential tests which are shown to have a substantial “saving” in the average sample sizes compared to the corresponding well known fixed-sample size procedures. We suggest, however, two separate methods of defining the “saving” and work primarily with one of these notions. We consider some special cases of some or all of the population means being known. In the cases k=2 and k=3, we have presented extensive numerical results through simulations showing the merits (in almost all the simulations) of our proposed procedures. Also, for k=2 we study various asymptotic behavior (as P*→1) of the stopping time involved in our statistical methods, and these are summarized in theorems 1 and 2. theorem 3 presents some partial asymptotic results (as P*→1) in the case of k=3. |
本系統中英文摘要資訊取自各篇刊載內容。