IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v25y1987ip83-93.html
   My bibliography  Save this article

On regular variation of probability densities

Author

Listed:
  • de Haan, L.
  • Resnick, S.

Abstract

Regular variation of the tail of a multivariate probability distribution is implied by regular variation of the density f provided f satisfies a regularity condition. We give a uniformity condition which controls variation of the function f across rays. Our condition is somewhat more flexible than the usual regularity condition of monotonicity. Some examples are given. As a by-product we get results on multidimensional regular variation of some independent interest.

Suggested Citation

  • de Haan, L. & Resnick, S., 1987. "On regular variation of probability densities," Stochastic Processes and their Applications, Elsevier, vol. 25, pages 83-93.
    • Handle: RePEc:eee:spapps:v:25:y:1987:i::p:83-93
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(87)90191-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    2. Cai, J., 2012. "Estimation concerning risk under extreme value conditions," Other publications TiSEM a92b089f-bc4c-41c2-b297-c, Tilburg University, School of Economics and Management.
    3. Cai, J. & Einmahl, J.H.J. & de Haan, L.F.M., 2011. "Estimation of extreme risk regions under multivariate regular variation," Other publications TiSEM b7a72a8d-f9bc-4129-ae9b-a, Tilburg University, School of Economics and Management.
    4. Li, Haijun & Hua, Lei, 2015. "Higher order tail densities of copulas and hidden regular variation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 143-155.
    5. Das, Bikramjit & Fasen-Hartmann, Vicky, 2024. "On heavy-tailed risks under Gaussian copula: The effects of marginal transformation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    6. Bikramjit Das & Tiandong Wang & Gengling Dai, 2022. "Asymptotic Behavior of Common Connections in Sparse Random Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2071-2092, September.
    7. Yun, Seokhoon, 1997. "On Domains of Attraction of Multivariate Extreme Value Distributions under Absolute Continuity," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 277-295, November.
    8. Yi He & John H. J. Einmahl, 2017. "Estimation of extreme depth-based quantile regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 449-461, March.
    9. Anand Deo & Karthyek Murthy, 2020. "Optimizing tail risks using an importance sampling based extrapolation for heavy-tailed objectives," Papers 2008.09818, arXiv.org.
    10. Omey, Edward & Van Gulck, Stefan, 2015. "Intuitive approximations in discrete renewal theory, Part 1: Regularly varying case," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 68-74.
    11. Tiandong Wang & Sidney I. Resnick, 2018. "Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 1029-1042, September.

    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:spapps:v:25:y:1987:i::p:83-93. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/505572/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.