Ziggurat

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 33 articles )

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  1. Minh, Nguyen Dang; To Duc, Khanh; Tuan, Nguyen Huy; Trong, Dang Duc: A two-dimensional backward heat problem with statistical discrete data (2018)
  2. Nane, Erkan; Tuan, Nguyen Huy: Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data (2018)
  3. Nowak, Piotr; Romaniuk, Maciej: Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making (2017)
  4. Karney, Charles F.F.: Sampling exactly from the normal distribution (2016)
  5. Riesinger, Christoph; Neckel, Tobias; Rupp, Florian: Solving random ordinary differential equations on GPU clusters using multiple levels of parallelism (2016)
  6. Rakshit, Pratyusha; Konar, Amit: Differential evolution for noisy multiobjective optimization (2015)
  7. Ceperic, Vladimir; Gielen, Georges; Baric, Adrijan: Sparse varepsilon $\varepsilon$-tube support vector regression by active learning (2014) ioport
  8. Meng, Xiangrui; Saunders, Michael A.; Mahoney, Michael W.: LSRN: A parallel iterative solver for strongly over- or underdetermined systems (2014)
  9. Voss, Jochen: An introduction to statistical computing. A simulation-based approach (2014)
  10. Fulger, Daniel; Scalas, Enrico; Germano, Guido: Random numbers from the tails of probability distributions using the transformation method (2013)
  11. Kalke, S.; Richter, W.-D.: Simulation of the $p$-generalized Gaussian distribution (2013)
  12. Manceur, Ameur M.; Dutilleul, Pierre: Maximum likelihood estimation for the tensor normal distribution: Algorithm, minimum sample size, and empirical bias and dispersion (2013)
  13. Tse, S.T.; Wan, Justin W.L.: Low-bias simulation scheme for the Heston model by inverse Gaussian approximation (2013)
  14. Bodini, Olivier; Roussel, Olivier; Soria, Michèle: Boltzmann samplers for first-order differential specifications (2012)
  15. 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
  16. Harriss-Phillips, W.M.; Bezak, E.; Yeoh, E.: The HYP-RT hypoxic tumour radiotherapy algorithm and accelerated repopulation dose per fraction study (2012)
  17. Üçer, E.; Söylemez, M.: Determination of minimum required damping in stochastic following seas modeled by using Gaussian white noise (2012)
  18. Chopin, Nicolas: Fast simulation of truncated Gaussian distributions (2011)
  19. Harman, Radoslav; Lacko, Vladimír: On decompositional algorithms for uniform sampling from $n$-spheres and $n$-balls (2010)
  20. Laud, Purushottam W.; Damien, Paul; Shively, Thomas S.: Sampling some truncated distributions via rejection algorithms (2010)

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