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On simulation and properties of the stable law

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  • Luc Devroye
  • Lancelot James

Abstract

The stable distribution, in its many parametrizations, is central to many stochastic processes. Many random variables that occur in the study of Lévy processes are related to it. Good progress has been made recently for simulating various quantities related to the stable law. In this note, we survey exact random variate generators for these distributions. Many distributional identities are also reviewed. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Luc Devroye & Lancelot James, 2014. "On simulation and properties of the stable law," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 307-343, August.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:3:p:307-343
    DOI: 10.1007/s10260-014-0260-0
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    References listed on IDEAS

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    1. Rafal Weron, 1996. "Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"," HSC Research Reports HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    2. R. C. H. Cheng & W. B. Liu, 1997. "Acknowledgement of Priority: A Continuous Representation of the Family of Stable Law Distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 729-729.
    3. Yano, Kouji & Yano, Yuko, 2008. "Remarks on the density of the law of the occupation time for Bessel bridges and stable excursions," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2175-2180, October.
    4. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    5. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    6. R. C. H. Cheng & W. B. Liu, 1997. "A Continuous Representation of the Family of Stable Law Distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 137-145.
    7. Devroye, Luc, 1984. "Methods for generating random variates with Polya characteristic functions," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 257-261, October.
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    Cited by:

    1. Mirko D’Ovidio & Federico Polito, 2014. "Discussion on the paper “On simulation and properties of the stable law” by L. Devroye and L. James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 359-363, August.
    2. Lucio Barabesi & Carolina Becatti & Marzia Marcheselli, 2018. "The Tempered Discrete Linnik distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 45-68, March.

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