IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v9y2007i4d10.1007_s11009-007-9021-y.html
   My bibliography  Save this article

Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

Author

Listed:
  • Djamel Meraghni

    (University Mohamed Khider)

  • Abdelhakim Necir

    (University Mohamed Khider)

Abstract

The characteristic exponent α of a Lévy-stable law S α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1

Suggested Citation

  • Djamel Meraghni & Abdelhakim Necir, 2007. "Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 557-572, December.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:4:d:10.1007_s11009-007-9021-y
    DOI: 10.1007/s11009-007-9021-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-007-9021-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-007-9021-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peng, L., 1998. "Asymptotically unbiased estimators for the extreme-value index," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 107-115, June.
    2. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    3. Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November.
    4. Rafał Weron, 2001. "Levy-Stable Distributions Revisited: Tail Index> 2does Not Exclude The Levy-Stable Regime," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 209-223.
    5. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    6. Neves, Claudia & Fraga Alves, M. I., 2004. "Reiss and Thomas' automatic selection of the number of extremes," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 689-704, November.
    7. Ana Ferreira & Casper G. de Vries, 2004. "Optimal Confidence Intervals for the Tail Index and High Quantiles," Tinbergen Institute Discussion Papers 04-090/2, Tinbergen Institute.
    8. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    9. Peng, Liang, 2001. "Estimating the mean of a heavy tailed distribution," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 255-264, April.
    10. Abdelhakim Necir, 2006. "A Nonparametric Sequential Test with Power 1 for the Mean of Lévy-stable Laws with Infinite Variance," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 321-343, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stachura Michał & Wodecka Barbara, 2022. "k-th record estimator of the scale parameter of the α-stable distribution," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 203-215, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brahimi, Brahim & Meraghni, Djamel & Necir, Abdelhakim & Zitikis, Ričardas, 2011. "Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 325-334.
    2. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
    3. Barunik, Jozef & Vacha, Lukas, 2010. "Monte Carlo-based tail exponent estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4863-4874.
    4. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    5. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    6. Liu, Qing & Peng, Liang & Wang, Xing, 2017. "Haezendonck–Goovaerts risk measure with a heavy tailed loss," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 28-47.
    7. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    8. Geluk, J. L. & Peng, Liang, 2000. "An adaptive optimal estimate of the tail index for MA(l) time series," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 217-227, February.
    9. Abdelhakim Necir, 2006. "A Nonparametric Sequential Test with Power 1 for the Mean of Lévy-stable Laws with Infinite Variance," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 321-343, September.
    10. Rassoul, Abdelaziz, 2013. "Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 698-703.
    11. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    12. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    13. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    14. Straetmans, Stefan & Chaudhry, Sajid M., 2015. "Tail risk and systemic risk of US and Eurozone financial institutions in the wake of the global financial crisis," Journal of International Money and Finance, Elsevier, vol. 58(C), pages 191-223.
    15. Igor Fedotenkov, 2013. "A bootstrap method to test for the existence of finite moments," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 315-322, June.
    16. Weron, Rafał, 2004. "Computationally intensive Value at Risk calculations," Papers 2004,32, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    17. Johann Lussange & Ivan Lazarevich & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2021. "Modelling Stock Markets by Multi-agent Reinforcement Learning," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 113-147, January.
    18. Candelon, Bertrand & Straetmans, Stefan, 2006. "Testing for multiple regimes in the tail behavior of emerging currency returns," Journal of International Money and Finance, Elsevier, vol. 25(7), pages 1187-1205, November.
    19. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    20. Taleb, Nassim Nicholas, 2009. "Errors, robustness, and the fourth quadrant," International Journal of Forecasting, Elsevier, vol. 25(4), pages 744-759, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:9:y:2007:i:4:d:10.1007_s11009-007-9021-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.