Related papers: Max-min dependence coefficients for Multivariate E…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
For independent random variables $(X_i)_{1\leq i\leq n}$, we consider the maximal correlation coefficient $R=R(\min_{i:1\leq i\leq m}X_i,\min_{j:\ell+1\leq j\leq n}X_j)$. If $X_1,X_2,\ldots,X_n$ are identically distributed with the same…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…
The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling…
We study the tail bound of the emperical covariance of multivariate normal distribution. Following the work of (Gittens & Tropp, 2011), we provide a tail bound with a small constant.
We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like…
Recursive max-linear vectors model causal dependence between its components by expressing each node variable as a max-linear function of its parental nodes in a directed acyclic graph and some exogenous innovation. Motivated by extreme…
This paper unifies and extends results on a class of multivariate Extreme Value (EV) models studied by Hougaard, Crowder, and Tawn. In these models both unconditional and conditional distributions are EV, and all lower-dimensional marginals…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…
The classical approach to multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction. This requires each marginal distribution be individually attracted to a univariate extreme…
The tail correlation function (TCF) is one of the most popular bivariate extremal dependence measures that has entered the literature under various names. We study to what extent the TCF can distinguish between different classes of…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
We consider the problem of risk diversification of $\alpha$-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to…
The classical tail dependence coefficient (TDC) may fail to capture non-exchangeable features of bivariate tail dependence since it evaluates the underlying copula only along the diagonal. To address this limitation, several measures of…
Impact assessment of natural hazards requires the consideration of both extreme and non-extreme events. Extensive research has been conducted on the joint modeling of bulk and tail in univariate settings; however, the corresponding body of…
Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend…
In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…