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研究生:李欣馨
研究生(外文):Lee, Hsin-Hsin
論文名稱:在型I設限下指數韋伯分配的參數估計
論文名稱(外文):Point Estimation for Exponentiated Weibull under type-I censoring
指導教授:陳思勉陳思勉引用關係
學位類別:碩士
校院名稱:輔仁大學
系所名稱:數學系研究所
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:2007
畢業學年度:95
語文別:英文
論文頁數:81
外文關鍵詞:Exponentiated Weibull distributionType-I censoringLINEX loss function
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  • 被引用被引用:0
  • 點閱點閱:300
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  • 下載下載:66
  • 收藏至我的研究室書目清單書目收藏:0
我們討論當資料受到型I設限時,指數韋伯分配兩個形狀參數和可靠度,以及累積失效函數的點估計,而估計方法則利用 (1) 最大概似估計式 (2) 廣義最大概似估計式,即事後最大概似函數絕對極大值產生之處,(3) 在LINEX損失函數和(4) 平方誤損失函數下的貝氏估計式。得到理論結果後,最後再輔以數值模擬分析方式,利用樣本均方差比較四種參數估計式之優劣。
In this thesis, we discuss point estimation of the two shape parameters, the reliability and the cumulative hazard function of an
Exponentiated Weibull distribution under type-I censoring. The following estimators are considered: (1) the maximum
likelihood estimator (2) the generalized maximum likelihood estimator (3) the Bayes estimators under squared-error loss
function and the LINEX loss function. Comparison among these estimators are made using Monte Carlo simulation study based on
their relative mean squared errors
1 Introduction 1
2 Parametric Approach - Maximum Likelihood Method 3
2.1 When alpha is known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 When alpha and theta are both unknown . . . . . . . . . . . . . . . . . . . . . . 6
3 Bayesian Approach 7
3.1 When alpha is known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1.1 Generalized Maximum Likelihood Estimator . . . . . . . . . . . 14
3.1.2 Bayes Estimator Under Squared-Error Loss Function . . . . . . . 15
3.1.3 Bayes Estimator Under LINEX Loss Function . . . . . . . . . . 17
3.2 When alpha and theta are independent random variables . . . . . . . . . . . . . . 21
3.2.1 Generalized Maximum Likelihood Estimator . . . . . . . . . . . 22
3.2.2 Bayes Estimator Under Squared-Error Loss Function . . . . . . . 23
3.2.3 Bayes Estimator Under LINEX Loss Function . . . . . . . . . . 28
3.3 When alpha and theta are dependent random variables . . . . . . . . . . . . . . . 30
3.3.1 Generalized Maximum Likelihood Estimator . . . . . . . . . . . 31
3.3.2 Bayes Estimator Under Squared-Error Loss Function . . . . . . . 32
3.3.3 Bayes Estimator Under LINEX Loss Function . . . . . . . . . . 37
4 Simulation Study 39
4.1 Parameter Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Conclusions and Suggestions 69
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[2] Choudhury, A., (2005). A simple derivation of moments of the exponentiated Weibull distribution. Metrika 62(1), pp. 17-22.
[3] Harry, F.M. and Ray, A.W., (1982). Bayesian Reliability Analysis; John Wiley and Sons: New York.
[4] Kotz, S., Johnson, N.L. and Read C.B., (1982) Encyclopedia of Statistical Sciences, Vol 1; A Wiley-Interscience Publication.
[5] Lindley, D.V., (1980). Approximate Bayesian method. Trabajos Estadistica 31, pp. 223-237.
[6] Lye, L.M., Happuarachchi, K.P. and Ryan, S., (1993). Bayes estimation of the Extreme-Value reliability function. IEEE Transactions on Reliability 42(4), pp. 641-644.
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