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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…

Statistics Theory · Mathematics 2024-05-01 Kai Wang , Chengxiu Ling

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…

Risk Management · Quantitative Finance 2016-04-12 Oliver Kley , Claudia Kluppelberg

For an m-dimensional multivariate extreme value distribution there exist 2^{m}-1 exponent measures which are linked and completely characterise the dependence of the distribution and all of its lower dimensional margins. In this paper we…

Statistics Theory · Mathematics 2012-11-01 Ioannis Papastathopoulos , Jonathan A. Tawn

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

Probability · Mathematics 2015-09-03 Helena Ferreira , Luísa Pereira , Ana Paula Martins

Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…

Methodology · Statistics 2025-07-16 Lorenzo Dell'Oro , Carlo Gaetan

Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…

Methodology · Statistics 2015-08-25 Boris Beranger , Simone A. Padoan

Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series $\mb{Y}_n$, ${n\geq 1}$, rescaled through random factors $\mb{T}_n$, ${n\geq 1}$, extending some…

Probability · Mathematics 2013-06-18 Helena Ferreira , Marta Ferreira

Let $\{X(t)= (X_1(t),X_2(t))^T,\ t \in \mathbb{R}^N\}$ be an $\mathbb{R}^2$-valued continuous locally stationary Gaussian random field with $\mathbb{E}[X(t)]=\mathbf{0}$. For any compact sets $A_1, A_2 \subset \mathbb{R}^N$, precise…

Probability · Mathematics 2015-11-13 Yuzhen Zhou , Yimin Xiao

A popular measure of association is the tail dependence coefficient which measures the strength of dependence in either the lower-left or upper-right tail of a bivariate distribution. In this paper, we develop the idea of quantile…

Statistics Theory · Mathematics 2024-02-09 A. Dastbaravarde , A. Dolati

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…

Statistics Theory · Mathematics 2012-10-05 John H. J. Einmahl , Andrea Krajina , Johan Segers

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…

Statistics Theory · Mathematics 2024-07-16 Stéphane Lhaut , Johan Segers

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…

Statistics Theory · Mathematics 2026-04-14 John H. J. Einmahl , Chen Zhou

Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case…

Methodology · Statistics 2017-01-31 Raphael Huser , Thomas Opitz , Emeric Thibaud

We consider random vectors $X$ that satisfy the equation in law $X=AX+B$, where $A$ is a given random diagonal matrix and $B$ a given random vector, both independent of $X$. It is well known by the works of Kesten and Goldie that the…

Probability · Mathematics 2025-10-28 Ewa Damek , Sebastian Mentemeier

The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has…

Methodology · Statistics 2018-10-02 Boris Beranger , Simone A. Padoan , Yangfan Xu , Scott A. Sisson

We consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable $Y$ and a nonnegative but otherwise arbitrary random variable $S$ called the…

Probability · Mathematics 2017-05-16 Leonardo Rojas-Nandayapa , Wangyue Xie

Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…

Statistics Theory · Mathematics 2018-07-18 Hanan Ahmed , John H. J. Einmahl

Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only if its radial part $R$ is regularly varying and is asymptotically independent of the angular…

Statistics Theory · Mathematics 2018-03-28 Phyllis Wan , Richard A. Davis

In this paper we are concerned with a sample of asymptotically independent risks. Tail asymptotic probabilities for linear combinations of randomly weighted order statistics are approximated under various assumptions, where the individual…

Probability · Mathematics 2014-06-24 Alexandru V. Asimit , Enkelejd Hashorva , Dominik Kortschak

The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these…

Statistics Theory · Mathematics 2020-07-09 Marta Ferreira , Ana Paula Martins , Helena Ferreira