This review paper focuses on statistical issues arising in modeling univariate extremes of a
random sample. In the last three decades there has been a shift from the area of parametric …

This comprehensive text gives an interesting and useful blend of the mathematical,
probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of …

Heavy-tailed distributions are often encountered in economics, finance, biology,
telecommunications, geology, etc. The heaviness of a tail is measured by a tail index …

In this paper we are interested in an adequate estimation of the dominant component of the
bias of Hill's estimator of a positive tail index γ, in order to remove it from the classical Hill …

In this paper we shall deal with the asymptotic and finite sample properties of “asymptotically
unbiased” estimators of the tail index γ, based on “external” adequate estimators of the …

We are interested in the derivation of the distributional properties of a weighted log-
excesses estimator of a positive tail index γ. One of the main objectives of such an estimator …

In this article, we are interested in the comparison, under a third-order framework, of classes
of second-order, reduced-bias tail index estimators, giving particular emphasis to minimum …

In this paper, we deal with bias reduction techniques for heavy tails, trying to improve mainly
upon the performance of classical high quantile estimators. High quantiles depend strongly …

In this article, we are interested in the direct estimation of the dominant component of the
bias of a classical tail index estimator, such as the Hill estimator, used here for illustration of …

Abstract In Statistics of Extremes we are mainly interested in the estimation of quantities
related to extreme events. In many areas of application, like for instance Insurance …