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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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1569-3961
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Volume 10, Issue 3-4

Issues

Smoothed Transformed Density Rejection*

Josef Leydold
  • Corresponding author
  • University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria, E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Wolfgang Hörmann
  • University of Economics and Business Administration, Department for Applied Statistics and Data Processing, Augasse 2-6, A-1090 Vienna, Austria, E-mail:
  • IE Department, Boğaziçi University Istanbul, 80815 Bebek-Istanbul, Turkey
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-05-09 | DOI: https://doi.org/10.1515/mcma.2004.10.3-4.393

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.

Keywords: Monte Carlo method; quasi-Monte Carlo method; nonuniform random variate generation; transformed density rejection; smoothed rejection; inversion MSC 65C05; 65C10; 65D30

About the article

Corresponding author: J. Leydold, Tel +43 1 313 36-4695. FAX +43 1 313 36-738


Published Online: 2008-05-09

Published in Print: 2004-12-01


Citation Information: Monte Carlo Methods and Applications mcma, Volume 10, Issue 3-4, Pages 393–401, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma.2004.10.3-4.393.

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