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 …

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

The main goal of this paper is to develop, under a semi-parametric context, asymptotically
normal estimators of the second order parameter ρ, a parameter related to the rate of …

The classical Hill estimator of a positive extreme value index (EVI) can be regarded as the
logarithm of the geometric mean, or equivalently the logarithm of the mean of order p= 0, of a …

Please see the supplementary material for an important correction. The main objective of
statistics of extremes lies in the estimation of quantities related to extreme events. In many …

The main objective of statistics of extremes is the prediction of rare events, and its primary
problem has been the estimation of the tail index γ, usually performed on the basis 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 …

Classical extreme value index estimators are known to be quite sensitive to the number k of
top order statistics used in the estimation. The recently developed second order reduced …

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 …

We present a class of semi-parametric estimators for the second order parameter related to
a probability distribution with a regularly varying tail. The second order parameter plays an …