A Log Probability Weighted Moment Estimator of Extreme Quantiles

  • Frederico CaeiroEmail author
  • Dora Prata Gomes
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 136)


In this paper we consider the semi-parametric estimation of extreme quantiles of a right heavy-tail model. We propose a new Probability Weighted Moment estimator for extreme quantiles, which is obtained from the estimators of the shape and scale parameters of the tail. Under a second-order regular variation condition on the tail, of the underlying distribution function, we deduce the non degenerate asymptotic behaviour of the estimators under study and present an asymptotic comparison at their optimal levels. In addition, the performance of the estimators is illustrated through an application to real data.


Extreme quantile Extreme value index Log probability weighted moment Optimal level Statistics of extremes  



Research partially supported by FCT – Fundação para a Ciência e a Tecnologia, project UID/MAT/00297/2013 (CMA/UNL), EXTREMA, PTDC/MAT /101736/2008.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.CMA and FCTUniversidade Nova de LisboaCaparicaPortugal

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