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

A network evolution with predicted tail and extremal indices of PageRank and the Max-
Linear Model used as node influence indices in random graphs is considered. The tail index …

This paper proposes a test to verify whether the k th moment of a random variable is finite.
We use the fact that, under general assumptions, sample moments either converge to a finite …

This paper reviews more than one hundred Pareto (and equivalent) tail index estimators. It
focuses on univariate estimators for nontruncated data. We discuss basic ideas of these …

We analyze the cluster structure in large networks by means of clusters of exceedances
regarding the influence characteristics of nodes. As the latter characteristics we use …

In this work, we backtest and compare, under the VaR risk measure, the fitting performances
of three classes of density distributions (Gaussian, Stable and Pareto) with respect to three …

For stationary time series with regularly varying marginal distributions, an important problem
is to estimate the associated tail index which characterizes the power‐law behavior of the …

The paper reviews the topic of extremal time series. The literature documenting the
presence of extremes in time series data is first reviewed, followed by a discussion of …

Consider a distribution $ F $ with regularly varying tails of index $-\alpha $. An estimation
strategy for $\alpha $, exploiting the relation between the behavior of the tail at infinity and of …

Heavy tail probability distributions are important in many scientific disciplines such as
hydrology, geology, and physics and therefore feature heavily in statistical practice. Rather …