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題名 常用統計套裝軟體的U(0,1)亂數產生器之探討
作者 張浩如
Chang, Hao-Ju
貢獻者 余清祥
張浩如
Chang, Hao-Ju
關鍵詞 亂數產生器
統計軟體
樣本平均蒙地卡羅法
Random number generator
Statistical software
sample-mean Monte Carlo method
日期 2000
上傳時間 31-Mar-2016 14:44:52 (UTC+8)
摘要 由於電腦的發展與普及，在各個領域的應用上，有越來越多的人利用電腦模擬的結果作為參考的依據。而在電腦模擬的過程中，亂數的產生是相當重要的一環。目前大多數的使用者都是直接利用套裝軟體內設的亂數產生器（random number generator）來產生亂數，但是在一般的文獻中對於各軟體內設的亂數產生器，則少有詳盡的探討。因此本論文的主要目的在於：針對SAS 6.12、SPSS 8.0、EXCEL 97、S-PLUS 2000及MINITAB 12等五種統計分析上常使用的套裝軟體，針對其內設U(0,1)亂數產生器進行較完整的介紹、比較、與探討。除了從週期長短、統計性質、電腦執行效率等三種不同觀點來評估這五種軟體內設亂數產生器的優劣之外，同時亦利用樣本平均蒙地卡羅法（sample-mean Monte Carlo method）在求解積分值上的表現作為電腦模擬的應用實例。
With the development and popularity of computers, in different fields more and more people are using the result from computer simulation as reference. The generation of random number is one of the most important factors in applying computer simulation. Nowadays most of users use intrinsic random number generators in software to produce random numbers. However, only a few articles focus on detailed comparisons of those random number generators. Thus, in this study, we explore the random number generators in frequently used statistical software; such as SAS 6.12, SPSS 8.0, EXCEL 97, S-PLUS 2000, MINITAB 12, etc. and discuss their performances in uniform (0,1) random number generators. This study focuses not only on the comparison of period length and statistical properties of these random number generators, but also on computer executive efficiency. In addition, we also use sample-mean Monte Carlo method as an integral example of computer simulation to evaluate these random number generators.
參考文獻 I. 中文書目
1. 林宏澤、林清泉編著，民80，系統模擬，台北市：高立圖書有限公司。
2. 唐惠欽著，民86，多階質數乘餘法亂數產生器之分析探討，國立成功大學工業管理研究所博士論文。
II. 英文書目
1. Barry, T. M. (1995), “Recommendations on the testing and use of pseudo-random number generators used in Monte Carlo analysis for risk assessment,”Risk analysis, 16, 93-105.
2. Bright, H. S., and Enison, R. L. (1979), “Quasi-random number sequences from a long-period TLP generator with remarks on application to cryptography, ” Comp.Surveys, 11, 357-370.
3. Casella, G., and Berger, R. L. (1990), Statistical Inference. Wadaworth, Inc., Belmont, California 94002,232-233.
4. Eichenauer, J., Grothe, H., and Lehn, J. (1988), “Marsaglia’s lattice test and non-linear congruential pseudo random generators, ” Metrika, 35, 241-250.
5. Fishman, G.S., and. Moore, L.R (1982), “A statistical evaluation of multiplicative congru-ential random number generators with modulus 231 - 1,” J. Amer. Statist. Assoc., 77, 129-136.
6. Fishman, G.S. (1990), “Multiplicative congruential random number generators with modulus : an exhaustive analysis for = 32 and a partial analysis for = 48,” Math. Comp., 54, 331-334.
7. Hull, T.E., and Dobell, A.R. (1962), “Random Number Generators,” SIAM Rev., 4,230-254.
8. Knuth, D. (1981), The Art of Computer Programming Volume 2: Semi-numerical Algorithms, Addison-Wesley, Reading, MA.
9. Law, A.M., and Kelton, W.D. (2000), Simulation Modeling and Analysis, 3d ed., McGraw-Hill.
10. L`Ecuyer, P. (1988), “Efficient and portable combined pseudo-random number generators,” Comm. ACM, 31, 742-749, 774.
11. L`Ecuyer, P. and Tezuka, S. (1991), “Structural properties for two classes of combined random number generators, ” Math. Comp., 57, 735-746.
12. L`Ecuyer, P. (1992), Testing random number generators, Proceeding of the 1992 Winter Simul. Conf., 305-313.
13. L`Ecuyer, P. (1994), “Uniform random numbers generation,” Ann. of Operations Res., 53, 77-120.
14. Lehmer, D.H. (1951), “Mathematical methods in large-scale computing units,” Proceedings of the Second Symposium on Large-Scale Digital Calculating Machinery. Harvard University Press, Cambridge, MA, 141-146.
15. Levene, H. (1952), “On the power function of tests of randomness based on runs up and down,” Ann. Math. Statistics, 23, 34-56.
16. Lewis, T. G., and Payne, W. H. (1973), “Generalized feedback shift register pseudorandom number alogrithm,” Journal of the ACM, 20, 456-458.
17. Marsaglia. G. (1968), “Random numbers fall mainly in the planes,” Proc. Nat. Acad. Sci.USA, 61, 25-211
18. Marsaglia, G. et al. (1973), “Random Number Package: "Super-Duper",” School of Computer Science, McGill University.
19. Marsaglia, G. (1985), “Matrices and the structure of random number sequences,” Linear algebraic and its appl., 67,147-156.
20. Marsaglia, G., Zaman, A., and Tsand, W.W. (1990), “Toward a universal random number generator,” Statistics & Proability Letters, 8, 35-39.
21. Matteis, A.D., and Pagnutti, S. (1988), “Parallelization of random number generators and long-range correlation,” Numer. Math., 53,595-608.
22. Montgomery, D.C. (1997), Design and analysis of experiments, Wiley, New York.
23. Moore, D. S. (1986), Tests of chi-squared type. In Goodness-of-Fit Techniques. New York: Marcel Dekker.
24. Neiderreiter H. (1991), “Recent trends in random number and random vector generation, ” Annals of Operations Research, 31, 323-346.
25. Ripley, B.D. (1987), Stochastic Simulation, Wiley, New York.
26. Ripley, B.D. (1999), Modern applied statistics with S-PLUS, Springer-Verlag, New York, 3rd.
27. Rubinstein, R.Y. (1981), Simulation and the Monte Carlo Method, John Wiley, New York.
28. Tausworthe, R.C. (1965), “Random numbers generated by linear recurrence modulo two,” Math. Camp.19, 201-209.
29. Wichmann, B. A., and Hill, J. D. (1982), “Algorithm AS183. An efficient and portable pseudo-random number generator,” Appl Statist. 31, 188-190; 33, 123.
30. Ziesel, H. (1986), “A remark on AS 183. An efficient and portable pseudo-random number generator,” Appl Statist. 35, 89.
描述 碩士
國立政治大學
統計學系
87354012
資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001943
資料類型 thesis
dc.contributor.advisor 余清祥zh_TW
dc.contributor.author (Authors) 張浩如zh_TW
dc.contributor.author (Authors) Chang, Hao-Juen_US
dc.creator (作者) 張浩如zh_TW
dc.creator (作者) Chang, Hao-Juen_US
dc.date (日期) 2000en_US
dc.date.accessioned 31-Mar-2016 14:44:52 (UTC+8)-
dc.date.available 31-Mar-2016 14:44:52 (UTC+8)-
dc.date.issued (上傳時間) 31-Mar-2016 14:44:52 (UTC+8)-
dc.identifier (Other Identifiers) A2002001943en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/83249-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 87354012zh_TW
dc.description.abstract (摘要) 由於電腦的發展與普及，在各個領域的應用上，有越來越多的人利用電腦模擬的結果作為參考的依據。而在電腦模擬的過程中，亂數的產生是相當重要的一環。目前大多數的使用者都是直接利用套裝軟體內設的亂數產生器（random number generator）來產生亂數，但是在一般的文獻中對於各軟體內設的亂數產生器，則少有詳盡的探討。因此本論文的主要目的在於：針對SAS 6.12、SPSS 8.0、EXCEL 97、S-PLUS 2000及MINITAB 12等五種統計分析上常使用的套裝軟體，針對其內設U(0,1)亂數產生器進行較完整的介紹、比較、與探討。除了從週期長短、統計性質、電腦執行效率等三種不同觀點來評估這五種軟體內設亂數產生器的優劣之外，同時亦利用樣本平均蒙地卡羅法（sample-mean Monte Carlo method）在求解積分值上的表現作為電腦模擬的應用實例。zh_TW
dc.description.abstract (摘要) With the development and popularity of computers, in different fields more and more people are using the result from computer simulation as reference. The generation of random number is one of the most important factors in applying computer simulation. Nowadays most of users use intrinsic random number generators in software to produce random numbers. However, only a few articles focus on detailed comparisons of those random number generators. Thus, in this study, we explore the random number generators in frequently used statistical software; such as SAS 6.12, SPSS 8.0, EXCEL 97, S-PLUS 2000, MINITAB 12, etc. and discuss their performances in uniform (0,1) random number generators. This study focuses not only on the comparison of period length and statistical properties of these random number generators, but also on computer executive efficiency. In addition, we also use sample-mean Monte Carlo method as an integral example of computer simulation to evaluate these random number generators.en_US
dc.description.tableofcontents 封面頁
證明書
致謝詞
論文摘要
目錄
第一章 緒論
第一節 研究動機與目的
第二節 論文架構
第二章 亂數產生器的方法
第一節 線性同餘法
第二節 移動暫存法
第三節 組合法
第三章 常用統計套裝軟體內設U(0,1)亂數產生的方法
第一節 SAS 6.12
第二節 SPSS 8.0
第三節 EXCEL 97
第四節 S-PLUS 2000
第五節 MINITAB 12
第四章 亂數產生器的比較方法
第一節 週期
第二節 統計檢定
2.1 均勻分配檢定
2.2 獨立性檢定
第三節 電腦執行
第四節 樣本平均蒙地卡羅法
第五章 分析結果
第一節 週期
第二節 統計檢定
2.1 亂數個數為500筆
2.2 亂數個數為1000筆
第三節 電腦執行
第四節 樣本平均蒙地卡羅法
第六章 結論與建議
第一節 結論
第二節 建議
參考文獻
附錄		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001943en_US
dc.subject (關鍵詞) 亂數產生器zh_TW
dc.subject (關鍵詞) 統計軟體zh_TW
dc.subject (關鍵詞) 樣本平均蒙地卡羅法zh_TW
dc.subject (關鍵詞) Random number generatoren_US
dc.subject (關鍵詞) Statistical softwareen_US
dc.subject (關鍵詞) sample-mean Monte Carlo methoden_US
dc.title (題名) 常用統計套裝軟體的U(0,1)亂數產生器之探討zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) I. 中文書目
1. 林宏澤、林清泉編著，民80，系統模擬，台北市：高立圖書有限公司。
2. 唐惠欽著，民86，多階質數乘餘法亂數產生器之分析探討，國立成功大學工業管理研究所博士論文。
II. 英文書目
1. Barry, T. M. (1995), “Recommendations on the testing and use of pseudo-random number generators used in Monte Carlo analysis for risk assessment,”Risk analysis, 16, 93-105.
2. Bright, H. S., and Enison, R. L. (1979), “Quasi-random number sequences from a long-period TLP generator with remarks on application to cryptography, ” Comp.Surveys, 11, 357-370.
3. Casella, G., and Berger, R. L. (1990), Statistical Inference. Wadaworth, Inc., Belmont, California 94002,232-233.
4. Eichenauer, J., Grothe, H., and Lehn, J. (1988), “Marsaglia’s lattice test and non-linear congruential pseudo random generators, ” Metrika, 35, 241-250.
5. Fishman, G.S., and. Moore, L.R (1982), “A statistical evaluation of multiplicative congru-ential random number generators with modulus 231 - 1,” J. Amer. Statist. Assoc., 77, 129-136.
6. Fishman, G.S. (1990), “Multiplicative congruential random number generators with modulus : an exhaustive analysis for = 32 and a partial analysis for = 48,” Math. Comp., 54, 331-334.
7. Hull, T.E., and Dobell, A.R. (1962), “Random Number Generators,” SIAM Rev., 4,230-254.
8. Knuth, D. (1981), The Art of Computer Programming Volume 2: Semi-numerical Algorithms, Addison-Wesley, Reading, MA.
9. Law, A.M., and Kelton, W.D. (2000), Simulation Modeling and Analysis, 3d ed., McGraw-Hill.
10. L`Ecuyer, P. (1988), “Efficient and portable combined pseudo-random number generators,” Comm. ACM, 31, 742-749, 774.
11. L`Ecuyer, P. and Tezuka, S. (1991), “Structural properties for two classes of combined random number generators, ” Math. Comp., 57, 735-746.
12. L`Ecuyer, P. (1992), Testing random number generators, Proceeding of the 1992 Winter Simul. Conf., 305-313.
13. L`Ecuyer, P. (1994), “Uniform random numbers generation,” Ann. of Operations Res., 53, 77-120.
14. Lehmer, D.H. (1951), “Mathematical methods in large-scale computing units,” Proceedings of the Second Symposium on Large-Scale Digital Calculating Machinery. Harvard University Press, Cambridge, MA, 141-146.
15. Levene, H. (1952), “On the power function of tests of randomness based on runs up and down,” Ann. Math. Statistics, 23, 34-56.
16. Lewis, T. G., and Payne, W. H. (1973), “Generalized feedback shift register pseudorandom number alogrithm,” Journal of the ACM, 20, 456-458.
17. Marsaglia. G. (1968), “Random numbers fall mainly in the planes,” Proc. Nat. Acad. Sci.USA, 61, 25-211
18. Marsaglia, G. et al. (1973), “Random Number Package: "Super-Duper",” School of Computer Science, McGill University.
19. Marsaglia, G. (1985), “Matrices and the structure of random number sequences,” Linear algebraic and its appl., 67,147-156.
20. Marsaglia, G., Zaman, A., and Tsand, W.W. (1990), “Toward a universal random number generator,” Statistics & Proability Letters, 8, 35-39.
21. Matteis, A.D., and Pagnutti, S. (1988), “Parallelization of random number generators and long-range correlation,” Numer. Math., 53,595-608.
22. Montgomery, D.C. (1997), Design and analysis of experiments, Wiley, New York.
23. Moore, D. S. (1986), Tests of chi-squared type. In Goodness-of-Fit Techniques. New York: Marcel Dekker.
24. Neiderreiter H. (1991), “Recent trends in random number and random vector generation, ” Annals of Operations Research, 31, 323-346.
25. Ripley, B.D. (1987), Stochastic Simulation, Wiley, New York.
26. Ripley, B.D. (1999), Modern applied statistics with S-PLUS, Springer-Verlag, New York, 3rd.
27. Rubinstein, R.Y. (1981), Simulation and the Monte Carlo Method, John Wiley, New York.
28. Tausworthe, R.C. (1965), “Random numbers generated by linear recurrence modulo two,” Math. Camp.19, 201-209.
29. Wichmann, B. A., and Hill, J. D. (1982), “Algorithm AS183. An efficient and portable pseudo-random number generator,” Appl Statist. 31, 188-190; 33, 123.
30. Ziesel, H. (1986), “A remark on AS 183. An efficient and portable pseudo-random number generator,” Appl Statist. 35, 89.		zh_TW