Advertisement

Doklady Mathematics

, Volume 100, Issue 2, pp 456–458 | Cite as

Inferences on Parametric Estimation of Distribution Tails

  • I. V. RodionovEmail author
MATHEMATICS
  • 6 Downloads

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.

Notes

FUNDING

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

REFERENCES

  1. 1.
    B. V. Gnedenko, Ann. Math. 44, 423–453 (1943).MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Pickands III, Ann. Stat. 3, 119–131 (1975).CrossRefGoogle Scholar
  3. 3.
    A. A. Balkema and L. de Haan, Ann. Probab. 2, 792–804 (1974).CrossRefGoogle Scholar
  4. 4.
    L. de Haan and L. Peng, Stat. Neerl. 52, 60–70 (1998).CrossRefGoogle Scholar
  5. 5.
    R. L. Smith, Ann. Stat. 15, 1174–1207 (1987).CrossRefGoogle Scholar
  6. 6.
    B. Hill, Ann. Stat. 3, 1163–1174 (1975).CrossRefGoogle Scholar
  7. 7.
    L. de Haan and A. Ferreira, Extreme Value Theory: An Introduction (Springer, New York, 2006).CrossRefGoogle Scholar
  8. 8.
    J. Beirlant, Y. Goegebeur, J. Teugels, and J. Segers, Statistics of Extremes: Theory and Applications (Wiley, New York, 2004).CrossRefGoogle Scholar
  9. 9.
    I. V. Rodionov, Probl. Inf. Transm. 54 (2), 124–138 (2018).MathSciNetCrossRefGoogle Scholar
  10. 10.
    I. V. Rodionov, Theory Probab. Appl. 63 (2), 327–335 (2018).MathSciNetCrossRefGoogle Scholar
  11. 11.
    I. V. Rodionov, Theory Probab. Appl. 63 (3), 364–380 (2019).MathSciNetCrossRefGoogle Scholar
  12. 12.
    J. Beirlant, M. Broniatowski, J. L. Teugels, and P. Vynckier, J. Stat. Plann. Inference 45, 21–48 (1995).CrossRefGoogle Scholar
  13. 13.
    N. Balakrishnan and M. Kateri, Stat. Probab. Lett. 78, 2971–2975 (2008).CrossRefGoogle Scholar
  14. 14.
    L. Gardes, S. Girard, and A. Guillou, J. Stat. Plann. Inference 141 (4), 429–444 (2009).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Steklov Mathematical Institute, Russian Academy of SciencesMoscowRussia
  2. 2.Trapeznikov Institute of Control Sciences, Russian Academy of SciencesMoscowRussia

Personalised recommendations