Related papers: On the Copula for multivariate Extreme Value distr…
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 show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and…
We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
We show that the set of $d$-variate symmetric stable tail dependence functions, uniquely associated with exchangeable $d$-dimensional extreme-value copulas, is a simplex and determine its extremal boundary. The subset of elements which…
The key result of this paper is to characterize all the multivariate symmetric Bernoulli distributions whose sum is minimal under convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli random…
Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…
We evaluate the dependence among the margins of a random vector with Multivariate Extreme Value distribution throughout the expected value of a range and relate this coefficient of dependence with the multivariate tail dependence. Its…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
Understanding multivariate extreme events play a crucial role in managing the risks of complex systems since extremes are governed by their own mechanisms. Conditional on a given variable exceeding a high threshold (e.g.\ traffic…
Extreme-value copulas arise as the limiting dependence structure of component-wise maxima. Defined in terms of a functional parameter, they are one of the most widespread copula families due to their flexibility and ability to capture…
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…
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…
We develop an asymptotic theory for extremes in decomposable graphical models by presenting results applicable to a range of extremal dependence types. Specifically, we investigate the weak limit of the distribution of suitably normalised…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector $X$ with continuous marginals. Said expressions appear explicit in the copula of $X$…
This paper develops a general inferential framework for discrete copulas on finite supports in any dimension. The copula of a multivariate discrete distribution is defined as Csiszar's I-projection (i.e., the minimum-Kullback-Leibler…