IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i5-6p437-444.html
   My bibliography  Save this article

Detecting finiteness in the right endpoint of light-tailed distributions

Author

Listed:
  • Neves, Cláudia
  • Pereira, António

Abstract

In Extreme Value statistics we often encounter testing procedures for assessing the presence of the Gumbel domain, attached to the simple null hypothesis of shape parameter [gamma]=0, thus praising the selection of extreme domains of attraction. However, the problem of assessing for light-tailed distributions with finite or infinite right endpoint is seldom referred. The latter is an impending problem of practical importance, particularly at the enrollment of subsequent estimation of extremal features such as small exceedance probabilities. In this paper, we present two test statistics whose asymptotic behavior, albeit under some restrictive yet reasonable conditions, enables us to distinguish light-tailed distribution functions with finite right endpoint from those with infinite endpoint lying in the Gumbel domain. An illustrative example is provided via application to significant wave height data recorded at Figueira da Foz, Portugal, from 1958 until 2001.

Suggested Citation

  • Neves, Cláudia & Pereira, António, 2010. "Detecting finiteness in the right endpoint of light-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 437-444, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:437-444
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00445-3
    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.

    References listed on IDEAS

    as
    1. Holger Drees, 1998. "On Smooth Statistical Tail Functionals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 187-210, March.
    2. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    3. Kim, Jin Seon & Yum, Bong-Jin, 2008. "Selection between Weibull and lognormal distributions: A comparative simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 477-485, December.
    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. Stéphane Girard & Armelle Guillou & Gilles Stupfler, 2012. "Estimating an endpoint with high-order moments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 697-729, 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. 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.
    2. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    3. de Haan, Laurens & Canto e Castro, Luisa, 2006. "A class of distribution functions with less bias in extreme value estimation," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1617-1624, September.
    4. Haoyu Chen & Tiantian Mao & Fan Yang, 2024. "Estimation of the Adjusted Standard-deviatile for Extreme Risks," Papers 2411.07203, arXiv.org.
    5. Jürg Hüsler & Deyuan Li, 2008. "Weak Convergence of the Empirical Mean Excess Process with Application to Estimate the Negative Tail Index," Methodology and Computing in Applied Probability, Springer, vol. 10(4), pages 577-593, December.
    6. Yongcheng Qi, 2010. "On the tail index of a heavy tailed distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 277-298, April.
    7. Jo~ao Nicolau & Paulo M. M. Rodrigues, 2024. "A simple but powerful tail index regression," Papers 2409.13531, arXiv.org.
    8. Yaolan Ma & Bo Wei & Wei Huang, 2020. "A nonparametric estimator for the conditional tail index of Pareto-type distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 17-44, January.
    9. Matheus Henrique Junqueira Saldanha & Adriano Kamimura Suzuki, 2023. "On dealing with the unknown population minimum in parametric inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 509-535, September.
    10. Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2021. "Local Robust Estimation of Pareto-Type Tails with Random Right Censoring," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 70-108, February.
    11. Einmahl, J.H.J. & Lin, T., 2003. "Asymptotic Normality of Extreme Value Estimators on C[0,1]," Discussion Paper 2003-132, Tilburg University, Center for Economic Research.
    12. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    13. 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.
    14. Sun, Haoze & Jiang, Yuexiang, 2014. "Empirical likelihood based confidence intervals for the tail index when γ<−1/2," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 149-157.
    15. Stupfler, Gilles & Yang, Fan, 2018. "Analyzing And Predicting Cat Bond Premiums: A Financial Loss Premium Principle And Extreme Value Modeling," ASTIN Bulletin, Cambridge University Press, vol. 48(1), pages 375-411, January.
    16. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    17. Rajkumar Bhimgonda Patil & Basavraj S Kothavale & Laxman Yadu Waghmode, 2019. "Selection of time-to-failure model for computerized numerical control turning center based on the assessment of trends in maintenance data," Journal of Risk and Reliability, , vol. 233(2), pages 105-117, April.
    18. 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.
    19. Dierckx, Goedele & Goegebeur, Yuri & Guillou, Armelle, 2013. "An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 70-86.
    20. Phornchanok Cumperayot & Casper G. de Vries, 2006. "Large Swings in Currencies driven by Fundamentals," Tinbergen Institute Discussion Papers 06-086/2, Tinbergen Institute.

    More about this item

    Statistics

    Access and download statistics

    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:80:y:2010:i:5-6:p:437-444. 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.