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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. Weron, Rafal, 1996. "Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables"," MPRA Paper 20761, University Library of Munich, Germany, revised 2010.
    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. 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.
    4. Devroye, Luc, 1984. "Methods for generating random variates with Polya characteristic functions," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 257-261, October.
    5. 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.
    6. 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.
    7. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
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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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