Related papers: Max-stable random sup-measures with comonotonic ta…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
This work investigates the tail behavior of solutions to the affine stochastic fixed-point equation of the form $X\stackrel{d}{=}AX+B$, where $X$ and $(A,B)$ are independent. Focusing on the light-tail regime, following [Burdzy et al.…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one…
In this paper, we introduce a novel model for the meta-analysis of proportions that integrates the standard random-effects model (REM) with an extreme value theory (EVT)-based component. The proposed model, named XT-REM (Extreme-Tail Random…
We provide conditions for the stochastic dominance comparisons of a risk $X$ and an associated risk $X+Z$, where $Z$ represents the uncertainty due to the environment and where $X$ and $Z$ can be dependent. The comparisons depend on both…
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…
Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric,…
In this paper, we introduce a new class of models for spatial data obtained from max-convolution processes based on indicator kernels with random shape. We show that this class of models have appealing dependence properties including tail…
Handling multiplicity without losing much power has been a persistent challenge in various fields that often face the necessity of managing numerous statistical tests simultaneously. Recently, $p$-value combination methods based on…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…
We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…
In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower…
Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…