Related papers: Extreme-Value Copulas
The modeling of dependence between maxima is an important subject in several applications in risk analysis. To this aim, the extreme value copula function, characterised via the madogram, can be used as a margin-free description of the…
We survey the connections between extreme-value theory and regular variation, in one and higher dimensions, from the algebraic point of view of our recent work on Popa groups.
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
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…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the…
Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of…
Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…
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…
This paper introduces an innovative method for constructing copula models capable of describing arbitrary non-monotone dependence structures. The proposed method enables the creation of such copulas in parametric form, thus allowing the…
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…
This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
In this paper, we continue Voiculescu's recent work on the analogous extreme value theory in the context of bi-free probability theory. We derive various equivalent conditions for a bivariate distribution function to be bi-freely…
Copulas are now frequently used to construct or estimate multivariate distributions because of their ability to take into account the multivariate dependence of the different variables while separately specifying marginal distributions.…
In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…
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…
The present article studies survival analytic aspects of semiparametric copula dependence models with arbitrary univariate marginals. The underlying survival functions admit a representation via exponent measures which have an…
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…