International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Non-uniform Random Variate Generations

  • Pierre L’Ecuyer
Reference work entry


As explained in the entry  Uniform Random Number Generators, the simulation of random variables on a computer operates in two steps: In the first step, uniform random number generators produce imitations of i.i.d. \(U(0,1)\)

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References and Further Reading

  1. Ahrens JH, Kohrt KD (1981) Computer methods for efficient sampling from largely arbitrary statistical distributions. Computing 26:19–31MATHMathSciNetGoogle Scholar
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  6. Chen HC, Asau Y (1974) On generating random variates from an empirical distribution. AIEE Trans 6:163–166Google Scholar
  7. Derflinger G, Hörmann W, Leydold J (2010) Random variate generation by numerical inversion when only the density is known. ACM Trans Model Comput Simul 20(4)Google Scholar
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  9. Devroye L (2006) Nonuniform random variate generation. In: Henderson SG, Nelson BL(eds) Simulation, handbooks in operations research and management science,  Chap. 4. Elsevier, Amsterdam, pp 83–121
  10. Glasserman P (2004) Monte Carlo methods in financial engineering. Springer, New YorkMATHGoogle Scholar
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  15. L’Ecuyer P (2004) Random number generation. In: Gentle JE, Haerdle W, Mori Y (eds) Handbook of computational statistics,  Chap. II.2, Springer, Berlin, pp 35–70
  16. L’Ecuyer P (2008) SSJ: a java library for stochastic simulation. Software user’s guide.
  17. L’Ecuyer P (2009) Quasi-Monte Carlo methods with applications in finance. Finance Stochastics 13(3):307–349MATHMathSciNetGoogle Scholar
  18. Law AM, Kelton WD (2000) Simulation modeling and analysis, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
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  20. von Neumann J (1951) Various techniques used in connection with random digits. In: Householder As et al (ed) The Monte Carlo method, vol 12. National Bureau of Standards Applied Mathematics Series, Washington, pp 36–38Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pierre L’Ecuyer
    • 1
  1. 1.Université de MontréalMontréalCanada