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Parameterizations and modes of stable distributions

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  • Nolan, John P.
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    Abstract

    The standard parameterizations used for stable distributions are poorly suited for both numerical work and for modeling. We suggest two parameterizations that are better for such purposes. The mode of a general stable density is numerically located and generalizations to multivariate stable laws are discussed.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-3TC1TF7-G/2/cc50260431c22102e2cc22d6be9d21f2
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 38 (1998)
    Issue (Month): 2 (June)
    Pages: 187-195

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    Handle: RePEc:eee:stapro:v:38:y:1998:i:2:p:187-195

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    Related research

    Keywords: Stable distributions Characteristic functions Stable modes Multivariate stable distributions;

    References

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    1. Gawronski WoLfgang & Wie├čner Martin, 1992. "Asymptotics And Inequalities For The Mode Of Stable Laws," Statistics & Risk Modeling, De Gruyter, vol. 10(1-2), pages 183-198, February.
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    Citations

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    Cited by:
    1. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2012. "The Japanese economy in crises: A time series segmentation study," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 6(5), pages 1-81.
    2. Koenker, Roger & Portnoy, Stephen, 2000. "Some pathological regression asymptotics under stable conditions," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 219-228, November.
    3. Enrico Scalas & Kyungsik Kim, 2006. "The art of fitting financial time series with Levy stable distributions," Papers physics/0608224, arXiv.org.
    4. Nolan, John P. & Ojeda-Revah, Diana, 2013. "Linear and nonlinear regression with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 186-194.
    5. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2011. "The Japanese economy in crises: A time series segmentation study," Economics Discussion Papers 2011-24, Kiel Institute for the World Economy.
    6. Fofack, Hippolyte & Nolan, John P., 2001. "Distribution of parallel exchange rates in African countries," Journal of International Money and Finance, Elsevier, vol. 20(7), pages 987-1001, December.
    7. Mitchell, James, 2002. "The use of non-normal distributions in quantifying qualitative survey data on expectations," Economics Letters, Elsevier, vol. 76(1), pages 101-107, June.
    8. Abdul-Hamid, Husein & Nolan, John P., 1998. "Multivariate Stable Densities as Functions of One Dimensional Projections," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 80-89, October.
    9. Matsui, Muneya & Takemura, Akimichi, 2009. "Integral representations of one-dimensional projections for multivariate stable densities," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 334-344, March.
    10. 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.

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