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研究生： 陳雪芳
論文名稱： 含瑕資料的估計 : 嚴正和分類
On the estimation of mixed exact and grouped data
指導教授： 李隆安
學位類別： 碩士
Master
系所名稱： 理學院 - 應用數學系
Department of Mathematical Sciences
論文出版年： 1991
畢業學年度： 79
語文別： 英文
論文頁數： 43
相關次數： 點閱：78  下載：0 
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    • Abstract

    This paper considers the estimation of data arisng from both grouped

    and exact forms. Several methods such as the Newton-Raphson, EM,

    and Kin-Zam methods are studied and compared. Especially, the

    method of Pao-Zhuan Yin-Yu is also. used to obtain UMVUE.

    CONTENT
    Chap. 1: Introduction………………..1
    Chap. 2: Statistical Considerations
    Section 1: Description of Data Set………………..4
    Section 2: Use of Newton-Raphson Method For MLEs………………..8
    Section 3: Review of Incomplete Data Method :
    Em Algorithm………………..11
    Chap. 3: Method of Kim-Zam
    Section 1: Desciption the Method of Kim-Zam………………..18
    Section 2: Apply the Method of Kim-Zam to Our Case………………..21
    Chap 4: Simulative Results and Discussion………………..24
    Chap 5: Method of Pao-Zhuan Yin-Yu
    Section 1: Describe the Method of Pao-Zhuan Yin-Yu………………..30
    Section 2: Statistical in Our Data Set………………..35
    Section 3: Numerical Experiments………………..41

    References

    [1] Archer, N. P. (1982). "Maximum Likelihood Estimation with Weibull Models When the Data Are Grouped". Commun. Statist. --Theor.Meth., 11(2),199-207.
    [2] Artamonovskii, V. P. (1988). "On Maximum Likelihood Estimation of the Shift and Scale Parameters Based on Grouped Samples".Theory of Prob. and its Appl., 33, 705-708.
    [3] Curtis, F. G. and Patrick, O. W. (1984). "Applied Numerical Analysis". Addison-Wesley, Reading, Mass. 3rd ed.
    [4] Dempster, A. P., Laird, N. M .. and Rubin, D. B. (1977). "Maximum Likelihood From Incomplete Data via the EM Algorithm". J. Roy.Statist. Soc. Ser. B 39, 1-38.
    [5] Hasselbland, V., Stead, A. G. and Galke, W. (1980) . "Analysis of Coarsely Grouped Data From the Lognormal Distribution". J. Amer.Statist. Ass, 75, 771-779.
    [6] Heitjan, D. F. (1989). "Inference From Grouped Continuous Data: A Review". Statist. Science, 4,164-181.
    [7] James C. Fu (1989). "Method of Kim-Zam : An Algorithm for Computing the Maximum Likelihood Estimator". Statistics and Probability Letters, 8, 289-296.
    [8] James C. Fu and Lung-An Li (1990). "Method of Pao-Zhuan YinYu : A Method of Stochastic Point Estimation".
    [9] McLaren, C. E, Brittenham, G. M. and Hasselblad, V. (1986)."Analysis of the Volume of Red Blood Cells : Application of the Expectation-Maximization Algorithm to Grouped Data From the Doubly-Truncated Lognormal Distribution". Biometrics, 42, 143-158.
    [10] Nelson, W. (1982). "Applied Life Data Analysis". Wiley, New York.
    [11] Ostrouchov, G. (1988). "Accuracy of Approximate Confidence Bounds Computed From Interval Censored Weibull and Lognormal Data". J. Statist. Comput. Simul. 29, 43-76.
    [12] Schader, M. and Schmid, F. (1988). "Small Sample Properties of the MLE of the Parameters μ and σ From a Grouped Sample of a Normal Population". Commun. Statist. -- Simula, 17, 229-239.
    [13] Sundberg, R. (1974). "Maximum Likelihood Theory for Incomplete Data From an Exponential Family". Second. J. Statist.,1,49-58.
    [14] Wei, D. and Shau, C.K. (1987). "Fitting and Optimal Grouping on Gamma Reliability Data". IEEE Transaction on Reliability, 36, 595-599.

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