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研究生： 張庭耀
Ting-yao Chang
論文名稱： 穩定型分布之參數的經驗分布估計法
Parameter Estimations for some stable Distributions based on Empirical Distributions
指導教授： 許玉生
Yu-Sheng Hsu
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 95
語文別： 英文
論文頁數： 28
中文關鍵詞： 經驗分布 、參數估計 、穩定型分布
外文關鍵詞： parametric estimation, Stable distribution, Empirical distribution
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    • 經驗分布在機率論及統計學都很重要，經驗分布為非母數統計之重要工具，本文研究經驗分布在母數統計之表現，以常態、柯西和Levy等穩定型分布為例，用經驗分布作參數估計並和常用統計量比較。

    Empirical distribution has important theoretical property like Glivenko-Cantelli theorem from which statistical inference for distribution function is possible. Empirical distribution is optimal in nonparametric framework. However, it is unknown if empirical distribution is optimal in parametric models. In this paper, we will investigate the efficiency of empirical distribution in parametric framework. The distributions considered include normal, Cauchy and Levy that are all stable.

    Section1.Introduction.....................................1 Section2.Parameter estimations for normal distributions based on empirical distributions.....................................2 Section3.Parameter estimations for Cauchy distributions based on empirical distributions.....................................9 Section4.Parameter estimations for Levy distributions based on empirical distributions......................................14 Section5.Conclusions.....................................19 References...............................................20 Appendix1................................................21 Appendix2................................................23 Appendix3................................................24 Appendix4................................................25 Appendix5................................................26

    [1]Pagan, A. and Ullah, A.(1999). "Nonparametric Econometrics," Cambridge University Press.
    [2]Prakasa Rao, B. L. S. (1983). "Nonparametric Functional
    Estimation," Academic Press.
    [3]Shorack and Wellner (1986). "Empirical Processes with Applications to Statistics," Wiley.
    [4]Silverman, B. W. (1986). "Density Estimation for Statistics and Data Analysis," Chapman and Hall.
    [5]Tapia, R. A. and Thompson, J. R. (1977). "Nonparametric Probability Density Estimation." Johns Hopkins University Press.

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