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研究生:鄔正豪
研究生(外文):Howard Wu
論文名稱:用經驗貝氏方法估計指數分配的失敗率
論文名稱(外文):Empirical Bayes Approach to Estimation of the Failure Rate in Exponential Distribution
指導教授:黎自奮
學位類別:碩士
校院名稱:國立中興大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
中文關鍵詞:可接受的最佳漸進經驗貝氏指數分配失敗率
外文關鍵詞:Admissibleasymptotic optimalityempirical Bayesexponential distributionfailure rate
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在經驗貝氏方法的背景下,我們取先驗分佈函數為加碼分配,以製造一個估計值來估計指數分配的失敗率,我們稱此估計值為經驗貝氏估計值( Empirical Bayes estimator )。此估計值符合可接受性(admissible )與最佳漸進( asymptotically optimal )這兩種性質。最後以蒙地卡羅模擬( Monte Carlo study )來驗證我們所推導的結果,此結果會是當樣本逼近無窮大時其值會逼近於貝氏估計值,如此可證明我們所推導的估計值具有最佳漸進的特性,進而證明用經驗貝氏估計值來估計指數分配的失敗率是合理的。

In the empirical Bayes (EB) decision problem consisting of squared error estimation of the failure rate in exponential distribution, a prior Λ is place on the gamma family of prior distributions to produce Bayes EB estimators which are admissible. A subclass of such estimators is shown to be asymptotically optimal (a.o.). The results of a Monte Carlo study are presented to demonstrate the a.o. property of the Bayes EB estimators.

中文摘要 …………………………………………………………. P.1
Abstract ………………………………………………………….. P.2
1.Introduction ……………………………………………. P.3
2.Bayes Empirical Bayes Estimation ……………………. P.6
3.Monte Carlo Simulation ……………………………….. P.17
4.Results …………………………………………………. P.18
5.References ……………………………………………... P.20

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21.Robbins, H. (1983). Jerzy Neyman memorial lecture-Some thoughts on empirical Bayes estimation, Ann. Statist., vol. 11, pp. 713-723.

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