Random Variable Generation

  • Christian P. Robert
  • George Casella
Part of the Springer Texts in Statistics book series (STS)

Abstract

The methods developed in this book mostly rely on the possibility of producing (with a computer) a supposedly endless flow of random variables (usually iid) for well-known distributions. Such a simulation is, in turn, based on the production of uniform random variables. Although we are not directly concerned with the mechanics of producing uniform random variables (see Note 2.6.1), we are concerned with the statistics of producing uniform and other random variables.

Keywords

Posterior Distribution Exponential Random Variable Uniform Random Variable Congruential Generator Random Variable Generation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. Marsaglia, G. and Zaman, A. (1993). The KISS generator. Technical report, Dept. of Statistics, Univ. of Florida.Google Scholar
  2. Knuth, D. (1981). The Art of Computer Programing. Volume 2: Seminumerical Algorithms (2nd edition). Addison-Wesley, Reading, MA.Google Scholar
  3. Rubinstein, R. (1981). Simulation and the Monte Carlo Method. John Wiley, New York.MATHCrossRefGoogle Scholar
  4. Ripley, B. (1987). Stochastic Simulation. John Wiley, New York.MATHCrossRefGoogle Scholar
  5. Fishman, G. (1996). Monte Carlo. Springer-Verlag, New York.MATHGoogle Scholar
  6. Ripley, B. (1987). Stochastic Simulation. John Wiley, New York.MATHCrossRefGoogle Scholar
  7. Marsaglia, G. and Zaman, A. (1993). The KISS generator. Technical report, Dept. of Statistics, Univ. of Florida.Google Scholar
  8. Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia.MATHCrossRefGoogle Scholar
  9. Yakowitz, S., Krimmel, J., and Szidarovszky, F. (1978). Weighted Monte Carlo integration. SIAM J. Numer. Anal., 15 (6): 1289–1300.MathSciNetMATHCrossRefGoogle Scholar
  10. Fang, K. and Wang, Y. (1994). Number-Theoretic Methods in Statistics. Chapman and Hall, New York.MATHGoogle Scholar
  11. Feller, W. (1971). An Introduction to Probability Theory and its Applications, volume 2. John Wiley, New York.MATHGoogle Scholar
  12. Billingsley, P. (1995). Probability and Measure. John Wiley, New York, third edition.MATHGoogle Scholar
  13. Devroye, L. (1985). Non-Uniform Random Variate Generation. Springer-Verlag, New York.Google Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Christian P. Robert
    • 1
  • George Casella
    • 2
  1. 1.CEREMADEUniversité Paris DauphineParis Cedex 16France
  2. 2.Department of StatisticsUniversity of FloridaGainesvilleUSA

Personalised recommendations