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研究生:林己迪
研究生(外文):Chi-Ti Lin
論文名稱:韋伯干擾下之迴歸模式推估
論文名稱(外文):Statistical Inference of a Simple Linear Regression Model with Weibull Disturbances
指導教授:陳重弘陳重弘引用關係
指導教授(外文):Chong-Hong Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
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:2003
畢業學年度:91
語文別:中文
論文頁數:30
中文關鍵詞:修正的最大概似法輪廓概似法韋伯分配
外文關鍵詞:Weibull DistributionModified maximum likelihoodProfile log-likelihood
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一般在線性迴歸模式 Y=θX+ε的估計裡,通常假設干擾項ε服從常態分配。但在許多的情況中,並非如此,例如,當資料表示的是存活時間或反應時間時,典型的ε卻是服從非對稱型態的分配。在本篇論文中,考慮模式中的干擾項服從韋伯分配。但在這樣的假設下,利用最大概似估計法來估計模式中的參數,總令人感到棘手。本文中將提出一修正的概似估計法,依此推得一修正的概似估計量,當然這樣的估算過程,是較容易計算的。並且此估計法亦可推得韋伯分配中形狀參數p的估計量,即在相同的資料下,相較於其他估計法,將可提供更多的訊息。
In a linear regression model, Y=θX+ε, it is often assumed that the random error ε is normally distributed. In numerous situations, e.g., when y is a measure of the life time or reaction time,ε typically has a skew distribution.We assume that ε has a Weibull distribution. For estimating the regress coefficientes, the maximum likelihood estimators are intractable. In the artical,
we derive modified likelihood estimators that have explicit algebraic forms and are, therefore, easier to compute. So that, we can obtain the estimator of shape parameter of Weibull distribution, through the method decrised above.
1 前言 5
2 迴歸模式 7
2.1 線性回歸模式...........7
2.2 韋伯分配及性質.........8
2.3 韋伯干擾...............9
3 模式之估計 11
3.1 概似估計..............11
3.2 最小平方估計..........13
3.3 Islam的修正概似估計...14
3.4 輪廓概似估計..........15
4 模擬 18
4.1 模擬方法..............18
4.2 模擬結果..............19
5 結論 19
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2.Bhattacharyya, G. K. (1985). "The asymptotics of maximum likelihood and related estimators based on Type II censored data." J. Amer. Stat. Assoc. , Vol. 80, pp.398-404.
3.Cohen, A. C. (1973). "The Reflected Weibull Distribution." Technometrics, Vol. 15 , pp. 867-873.
4.Cohen, A. C. and Whitlen, B. J. (1988). Parameter Estimation in Reliability and Life Span Models, Marcel Dekker , New York.
5.Fisher, R. A. and Tippett, L. H. C. (1950). Limiting Forms of the Frequency Distribution of the Large or Smallest Member of a Sample, Reprint in R. A. Fisher, Contributions to Nathernatical Statistics, John Whiley, New York.
6.Islam, M. Q. , Tiku, M. L. and Yildirim, F. (2001). "Nonnormal regression. I. Skew distributions." Commun. Stat. Theory and Meth. , Vol. 30 , pp. 993-1020.
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8.Lee, K. R. , Kapadia, C. H. and Dwight, B. B. (1980). "On estimating the scale parameter of Rayleigh distribution from censored samples" , Statist. Hefte, Vol. 21 , pp. 14-20
9.Nakagawa, T. and Osaki, S. (1975). The Discrete Weibull Distribution , IEEE Trans. On Reliability , R-24, pp.300-301.
10.Puthenpura, S. and Sinha, N. K. (1986). "Modified maximum likelihood method for the robust estimation of system parameters from very noisy data." Automatica. Vol. 22, pp. 231-235.
11.Robert, C. P. (1999). Monte Carlo statistical methods, Springer, New York.
12.Smith, R. L. (1985). "Maximum likelihood estimation in a class of non-regular cases." Biometrika , Vol. 72 , pp. 67-90.
13.Stafford, J. E. (1996). "A robust adjustment of the profile likelihood." Ann. Of Stat. , Vol. 24 No.1, pp. 336-352.
14.Tan, W. Y. and Balakrishnan, N. (1988). "Bayesian insight into Tiku''s robust procedure based on asymmetric censored samples." J. Stat. Comput. Simul. , Vol. 24 , pp. 17-31.
15.Tiku, M. L. (1967). "Estimating the mean and standard deviation from censored normal samples." Biometrika, Vol. 54 , pp. 155-165.
16.Tiku, M. L. (1968). "Estimating the parameters of normal and logistic distributions from censored samples." Australian J. Stat. , Vol. 10 , pp. 64-74.
17.Tiku, M. L. and Suresh, R. P. (1992). "A new method of estimation for location and scale parameters." J. Stat. Plann. Inf. , Vol. 30 , pp. 281-292.
18.Vaughan, D. C. and Tiku, M. L. (2000). "Estimation and hypothesis testing for a non-normal bivariate distribution and applications." J. Mathematical and Computer Modelling , Vol. 32 , pp. 53-67.
19.葉曉雯, (1991)"Identification of Weibull Distribution for Reliability Evaluation by Total Least Square Analysis" 碩士論文, 國立成功大學製造工程研究所.
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