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Smoothed Transformed Density Rejection

Author

Listed:
  • Leydold Josef

    (University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria, E-mail: Josef.Leydold@statistik.wu-wien.ac.at)

  • Hörmann Wolfgang

    (University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria, E-mail: Josef.Leydold@statistik.wu-wien.ac.at)

Abstract

There are situations in the framework of quasi-Monte Carlo integration where nonuniform low-discrepancy sequences are required. Using the inversion method for this task usually results in the best performance in terms of the integration errors. However, this method requires a fast algorithm for evaluating the inverse of the cumulative distribution function which is often not available. Then a smoothed version of transformed density rejection is a good alternative as it is a fast method and its speed hardly depends on the distribution. It can easily be adjusted such that it is almost as good as the inversion method. For importance sampling it is even better to use the hat distribution as importance distribution directly. Then the resulting algorithm is as good as using the inversion method for the original importance distribution but its generation time is much shorter.

Suggested Citation

  • Leydold Josef & Hörmann Wolfgang, 2004. "Smoothed Transformed Density Rejection," Monte Carlo Methods and Applications, De Gruyter, vol. 10(3-4), pages 393-401.
    • Handle: RePEc:bpj:mcmeap:v:10:y:2004:i:3-4:p:393-401:n:1021
    DOI: 10.1515/mcma.2004.10.3-4.393
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