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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/90100


    Title: GFSR亂數產生器的研究
    Authors: 范雅燕
    Contributors: 李子壩
    范雅燕
    Date: 1990
    1989
    Issue Date: 2016-05-03 14:13:56 (UTC+8)
    Abstract: 論文摘要
    無論是在社會科學或是自然科學的研究中，經常會面對複雜難解的問題，需要利用電腦模擬一些自然狀態，此時亂數就會被應用來增加其可靠性，被少人為主觀的控制因素。
    1973年Lewis & Payne 提出G F S R方法，這個方法所產生的擬隨機序列yt=O. atat+d........., t= 1 , 2 , .........。可以得到較線性除模法更長週期的序列，且可以改善在除模法中變數個數愈多，效果愈差的缺點，我們對此作理論上探討。
    此外，我們比較幾個G F S R 的實際製作演算法討論G F S R 的優缺點。最後本文將探討有關此產生器的應用，如在部份判別分析及在K - S 統計量的修正上。
    Reference: [l] A.C. Arvillias and D.G. Maritsas (1978) "Partitioning the Period of a Class of
    m-Sequence and Application to Pseudorandom Number Generation.",Journal of the ACM,
    Vol.25 , pp 675-686
    [2]Alexander Haas (1987)
    "The Multiple Prime Random Number Generator." ACM Transactions on Mathematical Software. Vol.13 .PP 368-381
    [3]R.J.Beckman and M.E.Johnson (1981)
    "A Ranking Procedure for Partial Discriminant Analysis.",Journal of the American Statistical
    Associatjon.Vol.76, pp 671-675
    [4]J.D.Broffitt.R.H.Randles and R.V.Hogg (1976)
    "Distribution-Free Partial Discriminant Analysis.",Journal of the American Statistical
    Association.Vol.7l , pp 934-939
    [5]Bruce Jay Collings (1987)
    "Compound Random Number Generators. ",Journal of the American Association.Vol.82 , pp 525-527
    [6]Bruce Jay Collings and G.Barry Hembree (1986)
    "Initializing Generalized Feedback Shift Register Pseudorandom Number Generators.",
    Journal of the ACH,Vol.33 , pp 706-711
    [7]R.R.Coveyou and R.D.Macpherson (1967)
    "Fourier Analysis of Uniform Random Number Generators.",Journal of the ACH,Vol.14 ,
    pp 100-119
    [8]Gentle and Kennedy (1980)
    Statistical Computing, Published by Marcel Dekker ,New York, Ch 6
    [9]Herbert S. Bright and Richard L. Enison (1979)
    "Quasi-Random Number Sequences from a Long-Period TLP Generator with Remarks on
    Application to Cryptography.",Computing Surveys ,Vol.ll ,pp 357-370
    [10]D . E.Knuth (1981)
    The Art of Computer Programming, V2 : Semi-numericalAlgorithms ,2nd Edition,
    Addison-Wesley, Reading ,Mass.
    [11]T.G.Lewis and W.H. Payne (1973)
    "Generalized Feedback Shift Register Pseudorandom Number Algorithm.",Journal of
    the ACM.Vol.20 .PP 456-468
    [12]W.H.Payne. J.R.Rdbung and T.P.Bogyo(1969)
    "Coding the Lehmer Pseudo-random Number Generator.", Communications of ACM.Vol.12 ?
    pp 85-86
    [13]W.H. Payne and K.L. McMillen (978)
    "Orderly Enumeration of Nonsingular Binary Matrices Applied to Text Encryption.".
    Communications of ACM.Vol.21, pp 259-263 [14]Marsaglia George (1984)
    "A Current View of Randow Number Generation.", Computer Science and Statistics: Sixteenth
    Symposiumon the Interface, Proceedings, pp 3-10
    [15]Marsaglia George and Liang-Huei-Tsay (1985)
    "Matrices and the Structure of Random Number Sequences.",Linear Algebra and its Appliations ,Vol.67,pp 147-156
    [16]Masanori Fushimi (1988)
    "Designing a Uniform Random Number Gererator Whose Subsequences are k-Distributed.",SIAM on Computing,Vol.17 , pp 89-99
    [17]M.Fushimi and S.Tezuka (1983)
    "The k-Distribution of Generalized Feedback Shift Register Pseudorandom Numbers."
    Communications of ACM , Vol.26 , pp 516-523
    [18] L.H.Miller (956)
    "Table of Percentage Points of Kolomogorov Statistics.",Journal of the American
    Statistical Association,Vol.51 , pp 111-121
    [19]Neal Zierler(1959)
    "Linear Recurring Sequence.",SIAM ,Vol.7 ,pp 31-48
    [20]R.C.Tauworthe (1965)
    "Random Numbers Generated by Linear Recurrence modulo Two.",Math. Compo. Vol.19, pp 201-209
    [21]J.P.R. Tootill,W.D.Robinsom and D.J.Eagle(1973)
    "An Asymptatically Random Tausworthe Sequence." Journal of the ACM , Vol.20 , pp 469-481
    [22]M.S.Weiss (1978)
    "Modifications of the Kolomogorov-Smirnov Statistic for use with correlated data.",
    Journal Df the American Statistical Association . Vol.73 .PP 872-875
    [23]何淮中（民76年3月）
    淺論隨機數列的方法，數學傳播11.1
    [24]林茂文（民75年10月)
    時間數列分析與預測，華泰書局
    [25]楊浩二（民73年月）
    多變量統計方法，華泰書局
    Description: 碩士
    國立政治大學
    統計學系
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002005376
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

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