Related papers: Extreme-Value Copulas

We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…

Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…

An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…

We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…

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…

The core of the classical block maxima method consists of fitting an extreme value distribution to a sample of maxima over blocks extracted from an underlying series. In asymptotic theory, it is usually postulated that the block maxima are…

We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail…

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…

Estimation of extreme value copulas is often required in situations where available data are sparse. Parametric methods may then be the preferred approach. A possible way of defining parametric families that are simple and, at the same…

There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…

For extreme value copulas with a known upper tail dependence coefficient we find pointwise upper and lower bounds, which are used to establish upper and lower bounds of the Spearman and Kendall correlation coefficients. We shown that in all…

We show that all multivariate Extreme Value distributions, which are the possible weak limits of the $K$ largest order statistics of iid sequences, have the same copula, the so called K-extremal copula. This copula is described through…

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…

The probabilistic characterization of the relationship between two or more random variables calls for a notion of dependence. Dependence modeling leads to mathematical and statistical challenges, and recent developments in extremal…

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…

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…

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…

Starting from the characterization of extreme-value copulas based on max-stability, large-sample tests of extreme-value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula…

Copulas are essential tools in statistics and probability theory, enabling the study of the dependence structure between random variables independently of their marginal distributions. Among the various types of copulas, Ratio-Type Copulas…

Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of…