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Remarks on the Stable S α (β,γ,μ) Distribution

Author

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  • Tibor K. Pogány

    (University of Rijeka)

  • Saralees Nadarajah

    (University of Manchester)

Abstract

Closed forms are derived for the probability density function (PDF) of the stable distribution S α (β, γ, μ), α ∈ (1, 2]. Consequent asymptotic expansions are given. Numerical evidence is given to show superior performance versus the most common way to compute a stable PDF.

Suggested Citation

  • Tibor K. Pogány & Saralees Nadarajah, 2015. "Remarks on the Stable S α (β,γ,μ) Distribution," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 515-524, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-014-9404-9
    DOI: 10.1007/s11009-014-9404-9
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    References listed on IDEAS

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    1. Muneya Matsui & Akimichi Takemura, 2004. "Some Improvements in Numerical Evaluation of Symmetric Stable Density and its Derivatives," CIRJE F-Series CIRJE-F-292, CIRJE, Faculty of Economics, University of Tokyo.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. 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.
    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    5. 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.
    6. Graham J. Worsdale, 1975. "Tables of Cumulative Distribution Functions for Symmetric Stable Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(1), pages 123-131, March.
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