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研究生:廖家賢
研究生(外文):Jia-Xian Liao
論文名稱:全項係數多項遞迴隨機數產生器
論文名稱(外文):ALL-TERMS-NONZERO MULTIPLE RECURSIVE GENERATOR
指導教授:蔡桂宏蔡桂宏引用關係
指導教授(外文):Gwei-Hung Tsai
學位類別:碩士
校院名稱:銘傳大學
系所名稱:應用統計資訊學系碩士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:86
中文關鍵詞:MDX-K-2DX-K-2廣義梅森質數多項遞迴法AX-K-1AX-K-1AAX-K-2
外文關鍵詞:MRGGMPDX-K-2AX-K-2AX-K-1AAX-K-1MDX-K-2
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目前很多科學與統計理論的模型發展常藉助電腦模擬。然而想得到較好的模擬結果,就需要使用性質優良的隨機數產生器。多項遞迴隨機數產生器(MRG)是目前擁有最長週期與高維度均等性且可考慮兼顧效率性的擬隨機數產生器,例如DX產生器。但DX-K-2產生器在所選取k個種子值中若有很多為0的狀況下會有離開0緩慢的缺點,例如DX-K-2產生器在所有種子值為 時,會連續產生k -2個0。本研究提出全項係數多項遞迴隨機數產生器,MDX-K-2, AX-K-2, AX-K-1, AX-K-1A四隨機數產生器可有效的改善DX-K-2產生器的缺點;AX-K-2, AX-K-1, AX-K-1A隨機數產生器則是具有效率性的隨機數產生器。使得全項係數多項遞迴產生器是一個有長週期、高維度均等性、效率性以及具較好的統計性質的隨機數產生器。最後在選取項數K為100下,與小於等於 並符合廣義梅森質數(GMP)條件時的質模數 ,列出MDX-K-2, AX-K-2,AX-K-1與AX-K-1A隨機數產生器可達最大週期的係數值。
The assistance of empirical studies based on computer-generated random numbers has become a common practice in enhancement of scientific and statistical theories. The results of simulation significantly support and improve the developing of statistical theory. However if we want to obtain better simulation results, we must employ superior random number generators. Multiple Recursive Generators are long periodic, high-dimensional equal distributed and could be efficient random number generators, such as DX generators. For an initial seed vector nearing zeros, DX generators may move too slowly away from zeros which might be a dramatically drawback. For example, if we use the initial vector (0, 0, ... , x, 0) for DX-k-2 generator, it should continually produce k-2 zeros. We provide a system of All-Terms-Nonzero Multiple Recursive Generators, MDX-K-2, AX-K-2, AX-K-1, and AX-K-1A that can improve the DX generator. All generators are not only high-dimensional, long periodic, and efficient but also with better statistical property. Finally, we present tables of coefficients for MDX-K-2, AX-K-2, AX-K-1, and AX-K-1A with terms k less than 100 and prime module p which is less than or equal to 2^31-1 and satisfying GMP test condition.
目錄
頁碼
致謝...............................................I
中文摘要..........................................II
英文摘要.........................................III
目 錄............................................IV
圖、表目錄........................................VI
檢測附錄目錄....................................VIII
附錄表目錄........................................IX
第一章 緒論........................................1
1.1 研究動機與背景……………………………….…………1
1.2 研究目的.......................................2
1.3 論文架構.......................................3
第二章 文獻探討....................................5
2.1實體的隨機數產生器..............................5
2.2非實體的電腦模擬隨機數產生器....................6
2.3檢測質多項式演算法介紹.........................18
第三章 研究方法--全項係數多項遞迴產生器...........23
3.1 MDX-K-2隨機數產生器...........................24
3.2 AX-K-2隨機數產生器............................30
3.3 AX-K-1隨機數產生器............................34
3.4 AX-K-1A隨機數產生器...........................37
第四章 產生器係數之選擇...........................40
4.1 MDX-K-2隨機數產生器之係數.....................41
4.2 AX-K-2隨機數產生器之係數......................43
4.3 AX-K-1隨機數產生器之係數......................46
4.4 AX-K-1A隨機數產生器之係數.....................48
第五章 結論與建議.................................51
5.1 結論..........................................51
5.2 未來研究與建議................................56
參考文獻..........................................58
檢測附錄..........................................62
附錄表............................................71
參考文獻
中文文獻:
[1] 蔣尚羽,MRG與MCG隨機數產生器之綜合探討-以低階項係數及矩陣實例說明-,銘傳大學應用統計資訊研究所碩士班論文,預計2007年六月發表.

[2] 陳峰彪,LCG係數的選擇與多重比較,銘傳大學應用統計資訊研究所碩士論文,2006.

[3] 孟祥仁,隨機數的統計檢定與比較,銘傳大學風險管理與統計資訊研究所碩士論文,2004.

英文參考文獻:
[1] Alanen, J. D. & Knuth, D. E. [1964], Tables of finite fields.
, A 26, 305–328.

[2] Deng, L. Y., [2006], Issues on Computer Search for Large Order Multiple Recursive Generators.

[3] Deng, L. Y., Li, H. & Tsai, G. H., [2005], Scalable parallel multiple recursive generators of large order.

[4] Deng, L. Y. [2004]. Generalized Mersenne Prime Number and Its Application to Random Number Generation, in Monte Carlo & Quasi-Monte Carlo methods 2002 (H. Niederreiter, ed.).

[5] Deng, L. Y. & Xu, H. Q. [2003], A System of High- dimensional, Efficient, Long-cycle and Portable Uniform Random Number Generators, ACM transactions on modeling and computer simulation, 13(4), 299-309.

[6] Deng, L. Y. & Xu, H. Q. [2002], A System of High- dimensional, Efficient, Long-cycle and Portable Uniform Random Number Generators, submitted.

[7] Deng, L. Y. & Lin, D. K. J. [2000], Random Number Generation for the New Century, American statistician, 54(2), 145-150.

[8] Deng, L.Y., Rousseau, C. & Yuan, Y. [1992], Generalized lehmer tausworthe random number generators, in Proceedings of the 30th annual ACM southeast regional conference, Raleigh, North Carolina, April 8-10, 108-115.

[9] Eichenauer, J., H. Grothe, and j. Lehn. [1988]. Marsaglia''s lattice test and non-linear congruential pseudo random number generators. Metrika 35: 241-250.

[10] Franklin, J. N. [1964], Equidistribution of matrix- power residues modulo one, Math. comp., 18, 560-568.

[11] Gleeson [2002] , Applied Physics Letters, Physics News Update no. 605

[12] Golomb, S. W. [1967], Shift Register Sequence, Holden-Day, San Francisco.

[13] Grothe, H. [1987], Matrix generators for pseudo-random vector generation, Statist. papers, 28, 233-238.

[14] James, F. [1990], A review of pseudorandom number generators, Comp. physics commu., 60, 329-344.

[15] Knuth, D. E. [1981], The Art of Computer Programming. Vol.2: seminumerical algorithms (2nd ed.), Addison-Wesley: Reading, MA.

[16] L’Ecuyer, P. [1997], Bad lattice structures for vectors of non-successive values produced by some linear recurrences. INFORMS Journal on Computing,9(1):57–60.

[17] L`Ecuyer, P. & Proulx, R. [1989], About polynomial–time “unpredictable” generators, Proc. of the 1989 winter simul. conf., 467-476.

[18] Lehmer, D. H. [1951], On large-scale digital calculating machinery (Proc. 2nd symp.), Cambridge: Harvard University Press.

[19] Lidl, R & H. Niederreiter [1986], Introduction to Finite Fields and Their Applications, Cambridge University Press: Cambridge.

[20] Marsaglia,G., [1990], Toward a universal random number generator. Statistics and Probability Letters, 9(1):35--39, 1990.

[21] Marsaglia, G., Zaman, A. & Tsang, W. W. [1990], Toward a universal random number generator, Stat. & prob. letters, 8, 35-39.

[22] Marsaglia, G. [1985], A current view of random number generation, Computer science and statistics, proceeding of sixteenth symposium on the interface, Atlanta, March 1984, Elsevier science publ. (North-Holland), 3-10.

[23] Marsaglia, G. & Tsay, L. H. [1985], Matrices and the structure of random number sequences, Linear algebraic and its appl., 67, 147-156.

[24] Marsaglia, G. [1968], Random number fall mainly in the planes, Proc. nat. acad. sci., 60, 25-28.

[25] Neiderreiter, H. [1993], Pseudorandom numbers and quasirandom points, Z angew. math mech, 73, T648-T652.

[26] Niederreiter, H. [1991], Recent Trends in Random Number and Rndom Vector Generation,” Annals of Operations Research, Vol. 31, 1991, pp. 323-346

[27] Niederreiter, H. [1988], Statistical independence of nonlinear congruential pseudorandom numbers, Monatsh math, 106, 149-159.

[28] Niederreiter, H. [1986], A pseudorandom vector generstor based on finite field arithmetic, Math. Japon, 31, 759-774.

[29] Ripley, B.D., [1987] Stochastic Simulation, New York, Wiley.

[30] Tausworthe, R. C. [1965], Random number generated by liner recurrence modulo two, Math comput, 19, 201-209.

[31] Wichmann, B.A. and I.D. Hill [1982], “ An efficient and portable pseudo-random number generator,” Appl. Statist., 31, 188-190.

[32] Zierler, N. [1959], “Linear recurring sequences,” J. SIAM, 7, 31-48.
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