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Good random number generators are (not so) easy to find

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  • Hellekalek, P.

Abstract

Every random number generator has its advantages and deficiencies. There are no “safe” generators. The practitioner's problem is how to decide which random number generator will suit his needs best. In this paper, we will discuss criteria for good random number generators: theoretical support, empirical evidence and practical aspects. We will study several recent algorithms that perform better than most generators in actual use. We will compare the different methods and supply numerical results as well as selected pointers and links to important literature and other sources. Additional information on random number generation, including the code of most algorithms discussed in this paper is available from our web-server under the address http://random.mat.sbg.ac.at/

Suggested Citation

  • Hellekalek, P., 1998. "Good random number generators are (not so) easy to find," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 46(5), pages 485-505.
    • Handle: RePEc:eee:matcom:v:46:y:1998:i:5:p:485-505
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    1. Winker, Peter & Fang, Kai-Tai, 1995. "Application of threshold accepting to the evaluation of the discrepancy of a set of points," Discussion Papers, Series II 248, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    2. L'Ecuyer, Pierre & Andres, Terry H., 1997. "A random number generator based on the combination of four LCGs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(1), pages 99-107.
    3. Pierre L'Ecuyer, 1996. "Combined Multiple Recursive Random Number Generators," Operations Research, INFORMS, vol. 44(5), pages 816-822, October.
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    1. Hawkins, Dollena S. & Allen, David M. & Stromberg, Arnold J., 2001. "Determining the number of components in mixtures of linear models," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 15-48, November.
    2. Aljahdali Asia & Mascagni Michael, 2017. "Feistel-inspired scrambling improves the quality of linear congruential generators," Monte Carlo Methods and Applications, De Gruyter, vol. 23(2), pages 89-99, June.
    3. Ovidiu Bagdasar & Minsi Chen & Vasile Drăgan & Ivan Ganchev Ivanov & Ioan-Lucian Popa, 2023. "On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators," Mathematics, MDPI, vol. 11(5), pages 1-16, March.
    4. Malinovskii, Vsevolod K. & Kosova, Ksenia O., 2014. "Simulation analysis of ruin capital in Sparre Andersen’s model of risk," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 184-193.
    5. L’Ecuyer, Pierre & Munger, David & Oreshkin, Boris & Simard, Richard, 2017. "Random numbers for parallel computers: Requirements and methods, with emphasis on GPUs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 3-17.
    6. Maximilian Beikirch & Torsten Trimborn, 2020. "Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model," Papers 2002.10222, arXiv.org.
    7. Tan, Syn Kiat & Guan, Sheng-Uei, 2009. "Randomness quality of permuted pseudorandom binary sequences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1618-1626.
    8. Kleiber Christian & Zeileis Achim, 2013. "Reproducible Econometric Simulations," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 89-99, July.
    9. Mascagni Michael & Hin Lin-Yee, 2013. "Parallel pseudo-random number generators: A derivative pricing perspective with the Heston stochastic volatility model," Monte Carlo Methods and Applications, De Gruyter, vol. 19(2), pages 77-105, July.
    10. Marchi, A. & Liverani, A. & Del Giudice, A., 2009. "Polynomial pseudo-random number generator via cyclic phase," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3328-3338.
    11. Ali Shakir Mahmood & Mohd Shafry Mohd Rahim & Nur Zuraifah Syazrah Othman, 2016. "Implementation of the Binary Random Number Generator Using the Knight Tour Problem," Modern Applied Science, Canadian Center of Science and Education, vol. 10(4), pages 1-35, April.
    12. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulator for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org, revised Oct 2018.
    13. Mascagni Michael & Hin Lin-Yee, 2012. "Parallel random number generators in Monte Carlo derivative pricing: An application-based test," Monte Carlo Methods and Applications, De Gruyter, vol. 18(2), pages 161-179, January.
    14. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    15. Tang, Hui-Chin, 2002. "Modified decomposition method for multiple recursive random number generator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(5), pages 453-458.
    16. Wegenkittl, Stefan, 2001. "Gambling tests for pseudorandom number generators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 281-288.
    17. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2019. "Robust Mathematical Formulation and Probabilistic Description of Agent-Based Computational Economic Market Models," Papers 1904.04951, arXiv.org, revised Mar 2021.

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