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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
 1.Bhattacharya, S. K. (1967). Bayesian approach to life testing and reliability estimation, J. Amer. Statist. Assoc., vol. 62, pp. 48-62.2.Bickel, P. J. and K. A. Doksum (1977). Mathematical Statistics: Basic Ideas and Selected Topics, Holden-Day Inc..3.Canavos, G. C. (1973). An empirical Bayes approach for the Poisson life distribution, IEEE Trans. Reliability, vol. R-22, pp. 91-96.4.Canavos, G. C. and C. P. Tsokos (1971). A study of ordinary and empirical Bayes approach to reliability estimation in the gamma life testing model, Proc. 1971 Annual Symp. Reliability, pp. 343-349.5.Deely, J.J. and D. V. Lindley (1981). Bayes empirical Bayes. J. Amer. Statist. Assoc. vol. 76, pp. 833-841.6.Good, I. J. (1965). The estimation of probabilities: An essay on modern Bayesian methods, Research Monograph No. 30, M.I.T. Press.7.Herman, R. J. and K. N. Patell (1971). Maximum likelihood estimation for multi-risk model, Technometrics, vol. 13(2), pp. 385-396.8.Holla, M. S. (1966). Bayesian estimates of reliability function, Australian J. Statist., vol. 8, pp. 32-35.9.Li, T. F. (1985). Bayes empirical Bayes estimation of a Poisson mean, Statist. And Probability Letters, pp. 309-313.10.Lin, K. J., J. S. Usher and F. M. Guess (1993). Exact maximum likelihood estimation using masked system data, IEEE Trans. Reliability, vol. 42, pp. 631-635.11.Lin, K. J., J. S. Usher and F. M. Guess (1996). Bayes estimation of component-reliability from masked system-life data, IEEE Trans. Reliability, vol. 45(2), pp. 233-237.2012.Maritz, J. S. (1966). Smooth empirical Bayes estimation for one-parameter discrete distribution, Biometrika, vol. 53, pp. 417-429.13.Maritz, J. S. (1967). Smooth empirical Bayes estimation for continuous distributions, Biometrika, vol. 54, pp. 435-450.14.Maritz, J. S. (1970). Empirical Bayes Methods, Methuen and Co., Ltd., London.15.Meeden, G. (1972). Some admissible empirical Bayes procedures, Ann. Math. Statist., vol. 43, pp. 96-101.16.Miyakawa, M. (1984). Analysis of incomplete data in a competing risk model, IEEE Trans. Reliability, vol. 33, pp. 293-296.17.Papadopoulos, A. S. (1978). The Burr distribution as a failure model from Bayesian approach, IEEE Trans. Reliability, vol. R-27, pp. 369-371.18.Pugh, E. L. (1963). The estimate of reliability in the exponential case, Operation Research (USA), vol. 11, pp. 57-61.19.Reiser, B., B. J. Flehinger and A. R. Conn (1996). Estimating component-defect probability from masked system success-failure data, IEEE Trans. Reliability, vol. 45(2), pp. 238-243.20.Robbins, H. (1956) An empirical Bayes approach to statistics. Proc. Third Berkeley Symp. Math. Statist. Pro. Vol. 1, University of California Press, pp. 157-163.21.Robbins, H. (1983). Jerzy Neyman memorial lecture-Some thoughts on empirical Bayes estimation, Ann. Statist., vol. 11, pp. 713-723.
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 1 遮蔽性設限資料之可靠度分析 2 檢定常態母體方差之經驗貝氏法

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 1 利用經驗貝氏法根據可靠度探討常態分布母體之擇優問題 2 利用經驗貝氏法根據可靠度探討伽瑪分布母體之擇優問題 3 經驗貝氏方法在重複基因微陣列晶片之應用 4 在圖型辨識中,利用經驗貝氏的方法來估計未知參數 5 基於多張原始影像的貝氏彩色濾光片內插補正法 6 對沖基金績效持續性檢定之比較─貝氏估計法vs.拔靴抽樣法 7 多變量t分佈的平均數與尺度共變異結構對於長期資料之貝氏聯合建模方法 8 類別資料混合先驗分配之經驗貝氏製程監控技術 9 國語單音統計辨認法 10 損壞個數之貝氏預測區間--以指數分配之設限資料為例 11 一個具不可信任修理站之可修理系統的貝氏分析 12 門檻隨機波動模型下風險值之經驗貝氏分析 13 類別資料在兩個經驗貝氏模型中的模型選取技術 14 成長曲線模型具群體變異數且為一般自相關共變異數結構之貝氏分析 15 利用貝氏方法於車牌辨識

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