SpringerLink
Log in

Inferences on Parametric Estimation of Distribution Tails

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

We propose a general method for parameter estimation of a distribution tail that does not depend on the fulfillment of the conditions of the Gnedenko theorem. We prove the consistency of the proposed estimator and its asymptotic normality under stronger conditions imposed on the parametric family of distribution tails. Additionally, the proposed method is adapted for estimating the Weibull and log-Weibull tail indices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.

Similar content being viewed by others

REFERENCES

  1. B. V. Gnedenko, Ann. Math. 44, 423–453 (1943).

    Article  MathSciNet  Google Scholar 

  2. J. Pickands III, Ann. Stat. 3, 119–131 (1975).

    Article  Google Scholar 

  3. A. A. Balkema and L. de Haan, Ann. Probab. 2, 792–804 (1974).

    Article  Google Scholar 

  4. L. de Haan and L. Peng, Stat. Neerl. 52, 60–70 (1998).

    Article  Google Scholar 

  5. R. L. Smith, Ann. Stat. 15, 1174–1207 (1987).

    Article  Google Scholar 

  6. B. Hill, Ann. Stat. 3, 1163–1174 (1975).

    Article  Google Scholar 

  7. L. de Haan and A. Ferreira, Extreme Value Theory: An Introduction (Springer, New York, 2006).

    Book  Google Scholar 

  8. J. Beirlant, Y. Goegebeur, J. Teugels, and J. Segers, Statistics of Extremes: Theory and Applications (Wiley, New York, 2004).

    Book  Google Scholar 

  9. I. V. Rodionov, Probl. Inf. Transm. 54 (2), 124–138 (2018).

    Article  MathSciNet  Google Scholar 

  10. I. V. Rodionov, Theory Probab. Appl. 63 (2), 327–335 (2018).

    Article  MathSciNet  Google Scholar 

  11. I. V. Rodionov, Theory Probab. Appl. 63 (3), 364–380 (2019).

    Article  MathSciNet  Google Scholar 

  12. J. Beirlant, M. Broniatowski, J. L. Teugels, and P. Vynckier, J. Stat. Plann. Inference 45, 21–48 (1995).

    Article  Google Scholar 

  13. N. Balakrishnan and M. Kateri, Stat. Probab. Lett. 78, 2971–2975 (2008).

    Article  Google Scholar 

  14. L. Gardes, S. Girard, and A. Guillou, J. Stat. Plann. Inference 141 (4), 429–444 (2009).

    Article  Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation, project no. 19-11-00290.

Author information

Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, 119333, Moscow, Russia

    I. V. Rodionov

  2. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 117997, Moscow, Russia

    I. V. Rodionov

Authors
  1. I. V. Rodionov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. V. Rodionov.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rodionov, I.V. Inferences on Parametric Estimation of Distribution Tails. Dokl. Math. 100, 456–458 (2019). https://doi.org/10.1134/S1064562419050156

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562419050156

Search

Navigation