Statistics and Computing

, Volume 1, Issue 2, pp 129–133 | Cite as

Efficient generation of random variates via the ratio-of-uniforms method

  • J. C. Wakefield
  • A. E. Gelfand
  • A. F. M. Smith


Improvements to the conventional ratio-of-uniforms method for random variate generation are proposed. A generalized radio-of-uniforms method is introduced, and it is demonstrated that relocation of the required density via the mode can greatly improve the computational efficiency of the method. We describe a multivariate version of the basic method and summarize a general strategy for efficient ratio-of-uniforms generation. Illustrative examples are given.


Ratio-of-uniforms power functions multivariate ratio-of-uniforms beta distribution Bayesian computation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cheng, A. C. H. and Feast, G. M. (1979) Some simple gamma variate generators.Applied Statistics,28, 290–295.Google Scholar
  2. Dagpunar, J. S. (1988)Principles of Random Variate Generation, Clarendon Press, Oxford.Google Scholar
  3. Devroye, L. (1986),Non-uniform Random Variate Generation, Springer-Verlag, New York.Google Scholar
  4. Gelfand, A. E. and Smith, A. F. M. (1990) Sampling based approaches to calculating marginal densities.Journal of the American Statistical Association,85, 398–409Google Scholar
  5. Kinderman, A. J. and Monahan, J. F. (1977) Computer generation of random variables using the ratio of random deviates.ACM Transactions in Mathematical Software,3, 257–260.Google Scholar
  6. Kinderman, A. J. and Monahan, J. F. (1980) New methods for generating student'st and gamma random variables.Computing,25, 369–377.Google Scholar
  7. Ripley, B. (1987)Stochastic Simulation, J. Wiley and Sons, New York.Google Scholar
  8. Smith, A. F. M. and Gelfand, A. E. (1991) Bayesian statistics without tears: a sampling-resampling perspective.American Statistician (forthcoming).Google Scholar

Copyright information

© Chapman & Hall 1991

Authors and Affiliations

  • J. C. Wakefield
    • 1
  • A. E. Gelfand
    • 2
  • A. F. M. Smith
    • 1
  1. 1.Department of MathematicsImperial CollegeLondonUK
  2. 2.Department of StatisticsUniversity of ConnecticutStorrsUSA

Personalised recommendations