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研究生： 鄭振成
Chen-Cheng Cheng
論文名稱： 以鑑別分析測量分布間之接近度
Measure the Closeness of Density Functions by Discriminant Analysis
指導教授： 許玉生
Yu-Sheng Hsu
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 95
語文別： 中文
論文頁數： 145
中文關鍵詞： 鑑別分析
外文關鍵詞： Discriminant Analysis
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    • 本文討論雙指數分布 ，柯西分布 ， 分布(其中 表自由度為4之 分布)和常態分布 之間的接近程度，我們以鑑別分析作為判斷的標準，基本概念如下：較接近常態分布之分布在作常態性鑑別分析時鑑別正確率應較接近常態分布之鑑別正確率。較接近雙指數分布之分布在作雙指數性鑑別分析時鑑別正確率應較接近雙指數分布之鑑別正確率。較接近柯西分布之分布在作柯西性鑑別分析時鑑別正確率應較接近柯西分布之鑑別正確率。我們將用計算機模擬方式比較鑑別正確率，藉以判斷分布間之接近程度。

    In this paper , we discuss the closeness of two density functions by discriminant analysis . The idea is as follows . Consider the discriminant analysis based on f , for those g that are close to f , the error rate of discriminantions for g will be close to error rate of discriminantions for f . We will make comparisons between transformed Normal , Double Exponential , Cauchy and t distributions by simulations .

    第一節 簡介......................................................................1 第二節 數據之模擬法.....................................................2 第三節 常態概似函數比之鑑別力分析.......................4 第四節 雙指數概似函數比之鑑別力分析...................6 第五節 柯西概似函數比之鑑別力分析.......................8 第六節 結論....................................................................10 參考文獻.............................................................................11 附錄一.................................................................................12 附錄1.1.....................................................................................12 附錄1.2.....................................................................................24 附錄二.................................................................................36 附錄2.1.....................................................................................36 附錄2.2.....................................................................................40 附錄三.................................................................................44 附錄3.1.....................................................................................44 附錄3.2.....................................................................................47 附錄四.................................................................................50 附錄4.1.....................................................................................50 附錄4.2.....................................................................................54 附錄五.................................................................................58 附錄5.1.....................................................................................58 附錄5.2.....................................................................................59 附錄六.................................................................................60 附錄6.1.....................................................................................60 附錄6.2.....................................................................................72 附錄七.................................................................................84 附錄7.1.....................................................................................84 附錄7.2.....................................................................................88 附錄八.................................................................................92 附錄8.1.....................................................................................92 附錄8.2.....................................................................................95 附錄九.................................................................................98 附錄9.1.....................................................................................98 附錄9.2...................................................................................102 附錄十...............................................................................106 附錄10.1.................................................................................106 附錄10.2.................................................................................107 附錄十一...........................................................................108 附錄11.1.................................................................................108 附錄11.2.................................................................................120 附錄十二...........................................................................132 附錄12.1.................................................................................132 附錄12.2.................................................................................136 附錄十三...........................................................................140 附錄13.1.................................................................................140 附錄13.2.................................................................................143

    [1]范雲雁(2006).以密度函數差及其平方之積分測量分布間之接近度.中央大學碩士論文初稿.
    [2]王楚元(2006).以適合度檢定測量分布間之接近度.中央大學碩士論文初稿.
    [3]Hogg,R.V. and Craig,A.T.(1995).Introduction to Mathematical Statistics. 5th ed. Prentice Hall.

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