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.

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References in zbMATH (referenced in 47 articles )

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  1. Aguiar e Oliveira, Hime jun.: Deterministic sampling from uniform distributions with Sierpiński space-filling curves (2022)
  2. Giles, Michael; Sheridan-Methven, Oliver: Analysis of nested multilevel Monte Carlo using approximate normal random variables (2022)
  3. Battaglia, Francesco; Cucina, Domenico; Rizzo, Manuel: Detection and estimation of additive outliers in seasonal time series (2020)
  4. Belov, A. A.; Kalitkin, N. N.; Tintul, M. A.: Unreliability of available pseudorandom number generators (2020)
  5. Kurita, Takamitsu: Likelihood-based tests for parameter constancy in (I(2)) CVAR models with an application to fixed-term deposit data (2020)
  6. Aletti, Giacomo: Generation of discrete random variables in scalable frameworks (2018)
  7. Bercin, Kutalmis M.; Xie, Zheng-Tong; Turnock, Stephen R.: Exploration of digital-filter and forward-stepwise synthetic turbulence generators and an improvement for their skewness-kurtosis (2018)
  8. Minh, Nguyen Dang; To Duc, Khanh; Tuan, Nguyen Huy; Trong, Dang Duc: A two-dimensional backward heat problem with statistical discrete data (2018)
  9. Nane, Erkan; Tuan, Nguyen Huy: Approximate solutions of inverse problems for nonlinear space fractional diffusion equations with randomly perturbed data (2018)
  10. Nguyen, Nguyet; Xu, Linlin; Ökten, Giray: A quasi-Monte Carlo implementation of the ziggurat method (2018)
  11. Spantini, Alessio; Bigoni, Daniele; Marzouk, Youssef: Inference via low-dimensional couplings (2018)
  12. Nowak, Piotr; Romaniuk, Maciej: Catastrophe bond pricing for the two-factor Vasicek interest rate model with automatized fuzzy decision making (2017)
  13. Sun, Yunpeng; Mendoza-Arriaga, Rafael; Linetsky, Vadim: Marshall-Olkin distributions, subordinators, efficient simulation, and applications to credit risk (2017)
  14. Karney, Charles F. F.: Sampling exactly from the normal distribution (2016)
  15. Loyola R, Diego G.; Pedergnana, Mattia; Gimeno García, Sebastián: Smart sampling and incremental function learning for very large high dimensional data (2016)
  16. McFarland, Christopher D.: A modified ziggurat algorithm for generating exponentially and normally distributed pseudorandom numbers (2016)
  17. Riesinger, Christoph; Neckel, Tobias; Rupp, Florian: Solving random ordinary differential equations on GPU clusters using multiple levels of parallelism (2016)
  18. Huthmacher, Klaus; Herzwurm, André; Gnewuch, Michael; Ritter, Klaus; Rethfeld, Baerbel: Monte Carlo simulation of electron dynamics in liquid water (2015)
  19. Rakshit, Pratyusha; Konar, Amit: Differential evolution for noisy multiobjective optimization (2015)
  20. Ceperic, Vladimir; Gielen, Georges; Baric, Adrijan: Sparse varepsilon (\varepsilon)-tube support vector regression by active learning (2014) ioport

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