IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v99y2015icp27-35.html
   My bibliography  Save this article

On large deviations of extremes under power normalization

Author

Listed:
  • Feng, Bo
  • Chen, Shouquan

Abstract

By using the theory of p-max stable laws, we study large deviations of the extremes under power normalization. The necessary and sufficient conditions for large deviations of each of the six p-max stable laws are derived.

Suggested Citation

  • Feng, Bo & Chen, Shouquan, 2015. "On large deviations of extremes under power normalization," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 27-35.
  • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:27-35
    DOI: 10.1016/j.spl.2015.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215000097
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2015.01.003?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. Drees, Holger & de Haan, Laurens & Li, Deyuan, 2003. "On large deviation for extremes," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 51-62, August.
    2. Subramanya, U. R., 1994. "On max domains of attraction of univariate p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 271-279, March.
    3. Christoph, Gerd & Falk, Michael, 1996. "A note on domains of attraction of p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 279-284, July.
    4. H. Barakat & E. Nigm & Magdy El-Adll, 2010. "Comparison between the rates of convergence of extremes under linear and under power normalization," Statistical Papers, Springer, vol. 51(1), pages 149-164, January.
    Full references (including those not matched with items on IDEAS)

    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. H. M. Barakat & E. M. Nigm, 2010. "On the rate of convergence to asymptotic independence between order statistics under power normalization with extension to the generalized order statistics," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(6), pages 703-714, December.
    2. Sha Jiang & Tingting Li & Xin Liao, 2018. "Distributional expansions on extremes from skew-normal distribution under power normalization," Statistical Papers, Springer, vol. 59(1), pages 1-20, March.
    3. Barakat, H.M. & Omar, A.R. & Khaled, O.M., 2017. "A new flexible extreme value model for modeling the extreme value data, with an application to environmental data," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 25-31.
    4. Geng Yang & Tingting Li, 2016. "Expansions on extremes from logarithmic general error distribution under power normalization," Statistical Papers, Springer, vol. 57(3), pages 781-793, September.
    5. H. M. Barakat & E. M. Nigm & O. M. Khaled & H. A. Alaswed, 2018. "The estimations under power normalization for the tail index, with comparison," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 431-454, July.
    6. Chen, Shouquan & Wang, Chao & Zhang, Geng, 2012. "Rates of convergence of extreme for general error distribution under power normalization," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 385-395.
    7. Weng, Zhichao & Liao, Xin, 2017. "Second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 33-43.
    8. E. Nigm, 2006. "Bootstrapping extremes of random variables under power normalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 257-269, June.
    9. H. Barakat & E. Nigm & Magdy El-Adll, 2010. "Comparison between the rates of convergence of extremes under linear and under power normalization," Statistical Papers, Springer, vol. 51(1), pages 149-164, January.
    10. Barakat, H.M. & El-Adll, Magdy E., 2009. "Asymptotic theory of extreme dual generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1252-1259, May.
    11. AL-Hussaini, Essam K. & El-Adll, Magdy E., 2004. "Asymptotic distribution of normalized maximum under finite mixture models," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 109-117, October.
    12. Bücher, Axel & Volgushev, Stanislav & Zou, Nan, 2019. "On second order conditions in the multivariate block maxima and peak over threshold method," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 604-619.
    13. Christoph, Gerd & Falk, Michael, 1996. "A note on domains of attraction of p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 279-284, July.
    14. Bhati, Deepesh & Ravi, Sreenivasan, 2017. "Some new characterizations of max domains of attraction of Fréchet and log-Fréchet laws under power normalization," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 92-99.
    15. A. S. Praveena & S. Ravi, 2023. "On the Exponential Max-Domain of Attraction of the Standard Log-Fréchet Distribution and Subexponentiality," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1607-1622, August.

    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:eee:stapro:v:99:y:2015:i:c:p:27-35. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.