Monte carlo techniques

  • S. Youssef
Reviews, Tables, And Plots Mathematical Tools or Statistics, Monte Carlo, Group Theory


Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions.


Probability Density Function Importance Sampling Monte Carlo Technique Random Angle Random Variate Generation 
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  1. 1.
    F. James, Comp. Phys. Coram.79 111 (1994), based on M. Lüscher, Comp. Phys. Comm. 79 100 (1994). This generator is available as the CERNLIB routine V115, RANLUX.zbMATHCrossRefADSGoogle Scholar
  2. 2.
    G. Marsaglia, A. Zaman, and W.W. Tsang,Towards a Universal Random Number Generator, Supercomputer Computations Research Institute, Florida State University technical report FSU- SCRI-87-50 (1987). This generator is available as the CERNLIB routine V113, RANMAR, by F. Carminati and F. James.Google Scholar
  3. 3.
    Much of DIEHARD is described in: G. Marsaglia,A Current View of Random Number Generators, keynote address,Computer Science and Statistics: 16th Symposium on the Interface, Elsevier (1985).Google Scholar
  4. 4.
    Newer generators with periods even longer than the lagged- Fibonacci based generator are described in G. Marsaglia and A. Zaman,Some Portable Very-Long-Period Random Number Generators, Compt. Phys.8, 117 (1994). The Numerical Recipes generatorran2 [W.H. Press and S.A. Teukolsky,Portable Random Number Generators, Compt. Phys.6, 521 (1992)] is also known to pass the DIEHARD tests.CrossRefGoogle Scholar
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    L. Devroye,Non-Uniform Random Variate Generation (Springer- Verlag, New York, 1986).zbMATHGoogle Scholar
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    Ch. Walck,Random Number Generation, University of Stockholm Physics Department Report 1987-10-20 (Vers. 3.0).Google Scholar
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    J.L. Leva, ACM Trans. Math. Softw.18 449 (1992). This generator has been implemented by F. James in the CERNLIB routine V120, RNORML.zbMATHCrossRefGoogle Scholar
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    F. James, Rept. on Prog, in Phys.43, 1145 (1980).CrossRefADSGoogle Scholar
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    13. This generator has been implemented by D. Drijard and K. Kölbig in the CERNLIB routine V136, RNPSSN.Google Scholar

Copyright information

© Springer-Verlag 2000

Authors and Affiliations

  • S. Youssef
    • 1
  1. 1.SCRIFlorida State UniversityUSA

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