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The Ziggurat Method for Generating Random Variables

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  • Marsaglia, George
  • Tsang, Wai Wan

Abstract

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

Suggested Citation

  • Marsaglia, George & Tsang, Wai Wan, 2000. "The Ziggurat Method for Generating Random Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i08).
    • Handle: RePEc:jss:jstsof:v:005:i08
    DOI: http://hdl.handle.net/10.18637/jss.v005.i08
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    Cited by:

    1. Ahmed Bensaida, 2012. "Improving the Forecasting Power of Volatility Models," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 2(3), pages 51-64, July.
    2. Hime Aguiar e Oliveira, 2022. "Deterministic sampling from uniform distributions with Sierpiński space-filling curves," Computational Statistics, Springer, vol. 37(1), pages 535-549, March.
    3. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    4. Nordahl, Helge A., 2008. "Valuation of life insurance surrender and exchange options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 909-919, June.
    5. Kurita, Takamitsu, 2020. "Likelihood-based tests for parameter constancy in I(2) CVAR models with an application to fixed-term deposit data," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    6. Nguyen Nguyet & Xu Linlin & Ökten Giray, 2018. "A quasi-Monte Carlo implementation of the ziggurat method," Monte Carlo Methods and Applications, De Gruyter, vol. 24(2), pages 93-99, June.
    7. Michele Azzone & Roberto Baviera, 2021. "A fast Monte Carlo scheme for additive processes and option pricing," Papers 2112.08291, arXiv.org, revised Jul 2023.
    8. Ran Li & Xiaomeng Duan & Yongfeng Lv, 2018. "Adaptive compressive sensing of images using error between blocks," International Journal of Distributed Sensor Networks, , vol. 14(6), pages 15501477187, June.
    9. Allin Cottrell, 2021. "Response surfaces for DF-GLS p-values," gretl working papers 8, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    10. repec:jss:jstsof:12:i07 is not listed on IDEAS
    11. Diaz-Emparanza, Ignacio, 2014. "Numerical distribution functions for seasonal unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 237-247.
    12. Leong, Philip H. W. & Zhang, Ganglie & Lee, Dong-U & Luk, Wayne & Villasenor, John, 2005. "A Comment on the Implementation of the Ziggurat Method," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i07).
    13. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    14. Yalta, A. Talha & Schreiber, Sven, 2012. "Random Number Generation in gretl," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(c01).
    15. Michele Azzone & Roberto Baviera, 2023. "A fast Monte Carlo scheme for additive processes and option pricing," Computational Management Science, Springer, vol. 20(1), pages 1-34, December.
    16. Roberto Baviera & Pietro Manzoni, 2024. "Fast and General Simulation of L\'evy-driven OU processes for Energy Derivatives," Papers 2401.15483, arXiv.org.
    17. Thomas W. Zuehlke, 2017. "Use of quadratic terms in Type 2 Tobit models," Applied Economics, Taylor & Francis Journals, vol. 49(17), pages 1706-1714, April.
    18. Huthmacher, Klaus & Herzwurm, André & Gnewuch, Michael & Ritter, Klaus & Rethfeld, Baerbel, 2015. "Monte Carlo simulation of electron dynamics in liquid water," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 242-251.
    19. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    20. Biswa Sengupta & Simon Barry Laughlin & Jeremy Edward Niven, 2014. "Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency," PLOS Computational Biology, Public Library of Science, vol. 10(1), pages 1-18, January.
    21. Yiran Chen & Giray Ökten, 2022. "A goodness-of-fit test for copulas based on the collision test," Statistical Papers, Springer, vol. 63(5), pages 1369-1385, October.
    22. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
    23. Emma Viviani & Luca Di Persio & Matthias Ehrhardt, 2021. "Energy Markets Forecasting. From Inferential Statistics to Machine Learning: The German Case," Energies, MDPI, vol. 14(2), pages 1-33, January.
    24. Rui Zhang & Lawrence M. Leemis, 2012. "Rectangles algorithm for generating normal variates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 52-57, February.

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