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Generation of correlated pseudorandom variables in Monte Carlo simulation

Wen De-Zhi Zhuo Ren-Hong Ding Da-Jie Zheng Hui Cheng Jing Li Zheng-Hong

Generation of correlated pseudorandom variables in Monte Carlo simulation

Wen De-Zhi, Zhuo Ren-Hong, Ding Da-Jie, Zheng Hui, Cheng Jing, Li Zheng-Hong
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  • Correlated pseudorandom variables with prescribed marginal distribution functions sometimes are required in simulation such as in Monte Carlo studies. In this paper, we present a general procedure and a simple but effective numerical approach to generating correlated random variables sampling sequence with prescribed marginal probability distribution functions and correlation coefficient matrix based on linear transformation-nonlinear transformation with Choesky factor. Some simulation results are reported. Simulation results show that the collections of random numbers generated by the presented procedure have desired correlations and pass the Kolmogorov-Smirnov non-parametric hypothesis test of specified marginal distribution. Some restrictions on the application of this method are discussed.
    [1]

    Pei Lu cheng 1989 Computer Stochastic Simulation (Changsha: Hunan Science and technology Press) p1 (in Chinese) [裴鹿成 1989 计算机随机模拟 (长沙: 湖南科学技术出版社) 第1页]

    [2]

    Xu S Y 2006 Monte Carlo Method and its Application in Nuclear Physics Experiment (2nd Ed.) (Beijing: Atomic Energy Press) p1 (in Chinese) [许淑艳 2006 蒙特卡罗方法在实验核物理中的应用 (第二版) (北京:原子能出版社) 第1页]

    [3]

    Ivan T D 2008 Monte Carlo Methods for Applied Scientists (Singapore: World Scientific Publishing Co. Pte. Ltd.) p1

    [4]

    Peter J 2002 Monte Carlo methods in finance (Chichester: John Wiley & Sons, Inc.) p1

    [5]

    Cox M G, Siebert B R L 2006 Metrologia 43 S178

    [6]

    Matthew N O S 2009 Monter Carlo Methods for Electromagnetics (Boca Raton: CRC Press Taylor & Francis Group)P1

    [7]

    Landau D P, Binder K 2000 A Guide to Monte Carlo Simulations in Statistical Physics (2nd Ed.) (New York: Cambridge University Press) p1

    [8]

    Ferguson D M, Siepmann J I, Truhlar D G 1999 Monte Carlo Methods in Chemical Physics (New York: John Wiley & Sons, Inc.) p1

    [9]

    Moonan W J 1957 J. Amer. Statist. Ass. 52 247

    [10]

    Box G E P, Muller M E 1958 Ann. Math. Statist. 29 610

    [11]

    Paul B, Fox B L, Linus E S (Translated by Yang Weigao) 1991 A guide to Simulation (Beijing: Science Press) p186 (in Chinese) [(美)布雷特利等著 杨惟高等译 1991 模拟导论(北京:机械工业出版社) 第186页]

    [12]

    Xu Z J 1985 Monte Carlo Method (Shanghai: Shanghai Science and Technology Press) p132 (in Chinese) 徐钟济 1985 蒙特卡罗方法上海:上海科学技术出版社 第132页)

    [13]

    Zhu B R 1987 Introduction to Monte Carlo Method (Ji-nan: Shandong University Press) p108 (in Chinese) [朱本仁 1987 蒙特卡罗方法引论 (济南: 山东大学出版社 第108页]

    [14]

    Niederreiter H 1992 Random Number Generation and Quasi-Monte Carlo Methods(Philadelphia: Society for Industrial and Applied Mathematics)P161

    [15]

    Rubinstein R, Kroese D P 2008 Simulation and the monte carlo method (2nd Ed.)(Hoboken: John Wiley & Sons, Inc.) p65

    [16]

    Kalos M H, Whitlock P A 2008 Monte Carlo Methods (2nd Ed.) (Weinheim: WILEY-VCH Verlag GmbH & Co.) p35

    [17]

    li S T, Hammond J L 1975 IEEE Transactions on Systems: Man, and Cybernetics SMC-5 557

    [18]

    Ronald L I, Conover W J 1982 Communications in Statistics-Simulation and Computation 11 311

    [19]

    Ronald L I, James M D 1982 Communications in Statistics-Simulation and Computation 11 335

    [20]

    Charles N H 1999 Risk Analysis 19 1205

    [21]

    Chen J T 2005 European Journal of Operational Research 167 226

    [22]

    Michael F 1999 Communications in Statistics-Simulation and Computation 28 785

    [23]

    Jing C 2005 M. S. Dissertation (Dalian: Dalian University of Technology) p31 (in Chinese) [金畅 2005 硕士学位论文(大连: 大连理工大学)第31页]

    [24]

    Wang Z K 1976 Probability theory and its application (1st Ed.) (Beijing: Science press) P105 (in Chinese) [王梓坤 1976 概率论基础及其应用(第一版)(北京:科学出版社) 第105页]

    [25]

    Salter M J, Ridler N M, Cox M G 2000 Technical Report CETM 22 (Teddington: National Physical Laboratory) p14

    [26]

    Nelsen R B 2006 An introduction to Copulas (2nd Ed.) (New York: Springer) p1

    [27]

    Zhang Y T 2002 Statistical Study 4 48 (in Chinese) [张尧庭 2002 统计研究 4 48]

  • [1]

    Pei Lu cheng 1989 Computer Stochastic Simulation (Changsha: Hunan Science and technology Press) p1 (in Chinese) [裴鹿成 1989 计算机随机模拟 (长沙: 湖南科学技术出版社) 第1页]

    [2]

    Xu S Y 2006 Monte Carlo Method and its Application in Nuclear Physics Experiment (2nd Ed.) (Beijing: Atomic Energy Press) p1 (in Chinese) [许淑艳 2006 蒙特卡罗方法在实验核物理中的应用 (第二版) (北京:原子能出版社) 第1页]

    [3]

    Ivan T D 2008 Monte Carlo Methods for Applied Scientists (Singapore: World Scientific Publishing Co. Pte. Ltd.) p1

    [4]

    Peter J 2002 Monte Carlo methods in finance (Chichester: John Wiley & Sons, Inc.) p1

    [5]

    Cox M G, Siebert B R L 2006 Metrologia 43 S178

    [6]

    Matthew N O S 2009 Monter Carlo Methods for Electromagnetics (Boca Raton: CRC Press Taylor & Francis Group)P1

    [7]

    Landau D P, Binder K 2000 A Guide to Monte Carlo Simulations in Statistical Physics (2nd Ed.) (New York: Cambridge University Press) p1

    [8]

    Ferguson D M, Siepmann J I, Truhlar D G 1999 Monte Carlo Methods in Chemical Physics (New York: John Wiley & Sons, Inc.) p1

    [9]

    Moonan W J 1957 J. Amer. Statist. Ass. 52 247

    [10]

    Box G E P, Muller M E 1958 Ann. Math. Statist. 29 610

    [11]

    Paul B, Fox B L, Linus E S (Translated by Yang Weigao) 1991 A guide to Simulation (Beijing: Science Press) p186 (in Chinese) [(美)布雷特利等著 杨惟高等译 1991 模拟导论(北京:机械工业出版社) 第186页]

    [12]

    Xu Z J 1985 Monte Carlo Method (Shanghai: Shanghai Science and Technology Press) p132 (in Chinese) 徐钟济 1985 蒙特卡罗方法上海:上海科学技术出版社 第132页)

    [13]

    Zhu B R 1987 Introduction to Monte Carlo Method (Ji-nan: Shandong University Press) p108 (in Chinese) [朱本仁 1987 蒙特卡罗方法引论 (济南: 山东大学出版社 第108页]

    [14]

    Niederreiter H 1992 Random Number Generation and Quasi-Monte Carlo Methods(Philadelphia: Society for Industrial and Applied Mathematics)P161

    [15]

    Rubinstein R, Kroese D P 2008 Simulation and the monte carlo method (2nd Ed.)(Hoboken: John Wiley & Sons, Inc.) p65

    [16]

    Kalos M H, Whitlock P A 2008 Monte Carlo Methods (2nd Ed.) (Weinheim: WILEY-VCH Verlag GmbH & Co.) p35

    [17]

    li S T, Hammond J L 1975 IEEE Transactions on Systems: Man, and Cybernetics SMC-5 557

    [18]

    Ronald L I, Conover W J 1982 Communications in Statistics-Simulation and Computation 11 311

    [19]

    Ronald L I, James M D 1982 Communications in Statistics-Simulation and Computation 11 335

    [20]

    Charles N H 1999 Risk Analysis 19 1205

    [21]

    Chen J T 2005 European Journal of Operational Research 167 226

    [22]

    Michael F 1999 Communications in Statistics-Simulation and Computation 28 785

    [23]

    Jing C 2005 M. S. Dissertation (Dalian: Dalian University of Technology) p31 (in Chinese) [金畅 2005 硕士学位论文(大连: 大连理工大学)第31页]

    [24]

    Wang Z K 1976 Probability theory and its application (1st Ed.) (Beijing: Science press) P105 (in Chinese) [王梓坤 1976 概率论基础及其应用(第一版)(北京:科学出版社) 第105页]

    [25]

    Salter M J, Ridler N M, Cox M G 2000 Technical Report CETM 22 (Teddington: National Physical Laboratory) p14

    [26]

    Nelsen R B 2006 An introduction to Copulas (2nd Ed.) (New York: Springer) p1

    [27]

    Zhang Y T 2002 Statistical Study 4 48 (in Chinese) [张尧庭 2002 统计研究 4 48]

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  • Received Date:  05 August 2011
  • Accepted Date:  14 June 2012
  • Published Online:  20 November 2012

Generation of correlated pseudorandom variables in Monte Carlo simulation

  • 1. Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900, China

Abstract: Correlated pseudorandom variables with prescribed marginal distribution functions sometimes are required in simulation such as in Monte Carlo studies. In this paper, we present a general procedure and a simple but effective numerical approach to generating correlated random variables sampling sequence with prescribed marginal probability distribution functions and correlation coefficient matrix based on linear transformation-nonlinear transformation with Choesky factor. Some simulation results are reported. Simulation results show that the collections of random numbers generated by the presented procedure have desired correlations and pass the Kolmogorov-Smirnov non-parametric hypothesis test of specified marginal distribution. Some restrictions on the application of this method are discussed.

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