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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 31-三月-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, 25-21118. 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 (作者) 張浩如 zh_TW dc.contributor.author (作者) Chang, Hao-Ju en_US dc.creator (作者) 張浩如 zh_TW dc.creator (作者) Chang, Hao-Ju en_US dc.date (日期) 2000 en_US dc.date.accessioned 31-三月-2016 14:44:52 (UTC+8) - dc.date.available 31-三月-2016 14:44:52 (UTC+8) - dc.date.issued (上傳時間) 31-三月-2016 14:44:52 (UTC+8) - dc.identifier (其他 識別碼) A2002001943 en_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) 87354012 zh_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/#A2002001943 en_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 generator en_US dc.subject (關鍵詞) Statistical software en_US dc.subject (關鍵詞) sample-mean Monte Carlo method en_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) thesis en_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, 25-21118. 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
