跳到主要內容

簡易檢索 / 詳目顯示

研究生: 李靜芳
Ching-Fang Lee
論文名稱: (X,Y)及max{X,Y}之分布及特徵函數之估計
Distribution and Characteristic Functions Estimations for (X,Y) and max{X,Y}
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: 91
語文別: 中文
論文頁數: 32
中文關鍵詞: 分布函數特徵函數經驗分布函數經驗特徵函數
外文關鍵詞: empirical distribution function, characteristic function, distribution function, empirical characteristic function
相關次數: 點閱:10下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 令X,Y表二獨立之隨機變數,則(X,Y)及max{X,Y}之分布及特徵函數各有兩種不同表示方式,也因此有二種不同估計方法,本文之主要目的在比較此二種估計法之優劣。


    Let X,Y be independent random variables. Distribution and characteristic functions for (X , Y) and max{X , Y} can be expressed by two different reports in each other. We will compare distribution and characteristic functions for (X , Y) and max{X , Y} in different estimation.

    第一節 簡介.................................1 第二節 經驗分布估計法 ......................3 第三節 經驗特徵函數估計法...................8 第四節 結論 ................................23 參考文獻 ..............................31

    1.ALEXAANDER, K. S.(1984).Probability inequalities for empirical processes and a law of the iterated logarithm.Ann.Probab.12 1041-1067. [Correction:(1987) Ann.Probab,15, 428-430.]
    2.BOLTHAUSEN,E.(1978)Weak convergence of an empirical process indexed by the
    closed convex subsets of I2.Z.Wahrsch.Verw.Gebiete ,43, 173-181.
    3.CSÖRGÖ,S.(1981).Multivariate empirical characteristic function.Z .Wahrsch .
    Verw.Gebiete, 55 ,203-229.
    4.CSÖRGÖ,S.(1981a).The empirical characteristic process when parameters are
    estimated. Contribution to Probability(Ed.J.Gani and V.K. Rohatgi),Academic Press, New York.
    5.CSÖRGÖ,S.(1981b).Limit behaviour of the empirical characteristic function. Ann.Probability ,9,130-144.
    6.CSÖRGÖ,S.(1983).Estimating characteristic functions under random censorship.
    Theory Probab.Appl,28,615-622.
    7.CSÖRGÖ,S.(1986).Testing for normality in arbitrary dimension.The Annals of
    Statistics. 14, 2,708-723.
    8.DAHLHAUS,R.(1988).Empirical spectral processes and their application to time
    series analysis.Stochastic Process.Appl.,30, 69-83.
    9.DUDLRY,R.M.(1978).Central limit theorems for empirical measures. Probab. 6,
    899-929.
    10.DUDLRY,R.M.(1984).A course on empirical processes.Ecole d’Et de Probabilities de Saint Flour XII. Lecture Notes in Math.1097,1-142.
    Springer,New York.
    11.EDDY,W.F.and HARTIGAN,J.A.(1977).Uniform convergence of the empirical
    distribution function over convex sets.Ann.Statist,5 ,370-374.
    12.FEIGIN,P.D.and HEATHCOTE,C.R.(1976).The empirical characteristic function
    and the Cramer-von Mises Statistic.Sankhya Ser .A ,38,309-325.
    13.FEUERVERGER, A. and MUREIKA, R.A.(1977). The empirical characteristic
    function and its applications.Ann. Statistic ,5,88-97.
    14.KELLER,H.-D.(1988).Large deviations of the empirical characteristic function.Acta Sci.Math.52,207-214.
    15.KENT,J.T.(1975).A weak convergence theorem for the empirical characteristic function.J.Appl.Prob.12,515-523.
    16.KOLCHINSKIĭ,V.I.(1989).Limit theorem for empirical characteristic functions in Banach spaces.Theor.Probability and Math.Statist.39,83-91.
    17.KOUTROUVELIS,I.A.(1980a).A goodness-of-fit test of simple hypotheses based on the empirical characteristic function.Biometrika.67,238-240.
    18.LUKACS,E.(1970).Characteristic Functions.Griffin,London.
    19.LUKACS,E.(1983).Developments in Characteristic Function Theory Griffin,London.
    20.MARCUS,M.B.(1981).Weak convergence of the empirical characteristic
    function .Ann.Probab.9,194-201.
    21.MUROTA,K.(1981).Test for normality based on the empirical characteristic
    function. Rep.Statist.Appl.Res.Un.Japan Sci.Engrs, 28 ,1-17
    22.MUROTA,K. and TAKEUCHI, K.(1981).The studentized empirical characteristic
    function and its application to test for the shape of distribution. Biometrika ,68 ,55-65.
    23.PETTITT,A.N.(1979).Testing for bivariate normality using the empirical
    distribution function.Comm.Statist.A—Theory Methods ,8,699-712.
    24.SHORACK,G.R.and WELLNER,J.A.(1986).Empirical Processes with Applications
    to Statistics.Wiley,New York.
    25.SORENSEN,H.(2002).Estimation of diffusion parameters for discretely observed
    diffusion processes.Bernoulli,8,491-508.
    26.USHAKOV,N.G.(1999).Selected topics in characteristic functions.VSP.
    27.WELSH,A.H.(1985).A note on scale estimates based on the empirical
    characteristic function and their application to test for normality.Statist.Probab.Letters 3.

    QR CODE
    :::