The Ziggurat Method for Generating Random Variables. We provide a new version of our ziggurat method for generating a random variable from a given decreasing density. It is faster and simpler than the original, and will produce, for example, normal or exponential variates at the rate of 15 million per second with a C version on a 400MHz PC. It uses two tables, integers ki, and reals wi. Some 99% of the time, the required x is produced by: Generate a random 32-bit integer j and let i be the index formed from the rightmost 8 bits of j. If j < k, return x = j x wi. We illustrate with C code that provides for inline generation of both normal and exponential variables, with a short procedure for settting up the necessary tables.

This software is also peer reviewed by journal JSS.

References in zbMATH (referenced in 29 articles )

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  1. Karney, Charles F.F.: Sampling exactly from the normal distribution (2016)
  2. Riesinger, Christoph; Neckel, Tobias; Rupp, Florian: Solving random ordinary differential equations on GPU clusters using multiple levels of parallelism (2016)
  3. Rakshit, Pratyusha; Konar, Amit: Differential evolution for noisy multiobjective optimization (2015)
  4. Ceperic, Vladimir; Gielen, Georges; Baric, Adrijan: Sparse varepsilon $\varepsilon$-tube support vector regression by active learning (2014) ioport
  5. Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.: LSRN: A parallel iterative solver for strongly over- or underdetermined systems (2014)
  6. Voss, Jochen: An introduction to statistical computing. A simulation-based approach (2014)
  7. Fulger, Daniel; Scalas, Enrico; Germano, Guido: Random numbers from the tails of probability distributions using the transformation method (2013)
  8. Kalke, S.; Richter, W.-D.: Simulation of the $p$-generalized Gaussian distribution (2013)
  9. Manceur, Ameur M.; Dutilleul, Pierre: Maximum likelihood estimation for the tensor normal distribution: Algorithm, minimum sample size, and empirical bias and dispersion (2013)
  10. Tse, S.T.; Wan, Justin W.L.: Low-bias simulation scheme for the Heston model by inverse Gaussian approximation (2013)
  11. Bodini, Olivier; Roussel, Olivier; Soria, Michèle: Boltzmann samplers for first-order differential specifications (2012)
  12. de Schryver, Christian; Schmidt, Daniel; Wehn, Norbert; Korn, Elke; Marxen, Henning; Kostiuk, Anton; Korn, Ralf: A hardware efficient random number generator for nonuniform distributions with arbitrary precision (2012) ioport
  13. Harriss-Phillips, W.M.; Bezak, E.; Yeoh, E.: The HYP-RT hypoxic tumour radiotherapy algorithm and accelerated repopulation dose per fraction study (2012)
  14. Üçer, E.; Söylemez, M.: Determination of minimum required damping in stochastic following seas modeled by using Gaussian white noise (2012)
  15. Chopin, Nicolas: Fast simulation of truncated Gaussian distributions (2011)
  16. Harman, Radoslav; Lacko, Vladimír: On decompositional algorithms for uniform sampling from $n$-spheres and $n$-balls (2010)
  17. Laud, Purushottam W.; Damien, Paul; Shively, Thomas S.: Sampling some truncated distributions via rejection algorithms (2010)
  18. Lutz, Björn: Pricing of derivatives on mean-reverting assets (2010)
  19. Anderson, Scot; Revesz, Peter: Efficient MaxCount and threshold operators of moving objects (2009) ioport
  20. Jonen, Christian: An efficient implementation of a least squares Monte Carlo method for valuing American-style options (2009)

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