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Detecting finiteness in the right endpoint of light-tailed distributions

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  • 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
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    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.
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    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.

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