Extreme-value copulas arise as the possible limits of copulas of component-wise maxima of independent, identically distributed samples. The use of bivariate extreme-value copulas is greatly facilitated by their representation in terms of Pickands dependence functions. The two main families of...

In a stationary sequence of random variables, high-threshold exceedances may cluster together. Two approximations of such a clusters distribution are established. These justify and generalize sampling schemes for clusters of extremes already known for Markov chains

For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold. The approximations are in terms of the distribution of the process conditionally on the event...

In the sixties Mandelbrot already showed that extreme price swings are more likely than some of us think or incorporate in our models. A modern toolbox for analyzing such rare events can be found in the field of extreme value theory. At the core of extreme value theory lies the modelling of...

Classical extreme-value theory for stationary sequences of random variables can up to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts...

We establish Edgeworth expansions for the distribution function of the centered and normalized Hill estimator for the reciprocal of the index of regular variation of the tail of a distribution function.The expansions are used to derive expansions for coverage probabilities of confidence...

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated...

At the heart of the copula methodology in statistics is the idea of separating marginal distributions from the dependence structure. However, as shown in this paper, this separation is not to be taken for granted: in the model where the copula is known and the marginal distributions are...