International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Non-uniform Random Variate Generations

  • Pierre L’Ecuyer
Reference work entry
DOI: https://doi.org/10.1007/978-3-642-04898-2_408

Introduction

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. \(U(0,1)\)

This is a preview of subscription content, log in to check access.

References and Further Reading

  1. Ahrens JH, Kohrt KD (1981) Computer methods for efficient sampling from largely arbitrary statistical distributions. Computing 26:19–31zbMATHMathSciNetGoogle Scholar
  2. Asmussen S, Glynn PW (2007) Stochastic simulation. Springer, New YorkzbMATHGoogle Scholar
  3. Bertoin J (1996) Lévy Processes. Cambridge University Press, CambridgezbMATHGoogle Scholar
  4. Blair JM, Edwards CA, Johnson JH (1976) Rational Chebyshev approximations for the inverse of the error function. Math Comput 30:827–830zbMATHMathSciNetGoogle Scholar
  5. Brent RP (1973) Algorithms for minimization without derivatives. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  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
  8. Devroye L (1986) Non-Uniform random variate generation. Springer, New YorkzbMATHGoogle Scholar
  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 YorkzbMATHGoogle Scholar
  11. Hörmann W, Derflinger G (2002) Fast generation of order statistics. ACM Trans Model Comput Simul 12(2):83–93Google Scholar
  12. Hörmann W, Leydold J (2003) Continuous random variate generation by fast numerical inversion. ACM Trans Model Comput Simul 13(4):347–362Google Scholar
  13. Hörmann W, Leydold J, Derflinger G (2004) Automatic nonuniform random variate generation. Springer, BerlinzbMATHGoogle Scholar
  14. Kinderman AJ, Monahan JF (1977) Computer generation of random variables using the ratio of uniform deviates. ACM Trans Math Softw 3:257–260zbMATHGoogle Scholar
  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. http://www.iro.umontreal.ca/~lecuyer
  17. L’Ecuyer P (2009) Quasi-Monte Carlo methods with applications in finance. Finance Stochastics 13(3):307–349zbMATHMathSciNetGoogle Scholar
  18. Law AM, Kelton WD (2000) Simulation modeling and analysis, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  19. Nelsen RB (1999) An introduction to Copulas. Lecture Notes in Statistics, vol 139. Springer, New YorkzbMATHGoogle Scholar
  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
  21. Walker AJ (1974) New fast method for generating discrete random numbers with arbitrary frequency distributions. Electron Lett 10:127–128Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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