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When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate…
The rich class of multivariate Pareto distributions forms the basis of recently introduced extremal graphical models. However, most existing literature on the topic is focused on the popular parametric family of H\"usler--Reiss…
Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…
The extreme value theory is very popular in applied sciences including Finance, economics, hydrology and many other disciplines. In univariate extreme value theory, we model the data by a suitable distribution from the general max-domain of…
When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the {generalised Pareto…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
Regular vine sequences permit the organisation of variables in a random vector along a sequence of trees. Regular vine models have become greatly popular in dependence modelling as a way to combine arbitrary bivariate copulas into…
Impact assessment of natural hazards requires the consideration of both extreme and non-extreme events. Extensive research has been conducted on the joint modeling of bulk and tail in univariate settings; however, the corresponding body of…
The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
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…
For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the…
Modelling multivariate extreme events is essential when extrapolating beyond the range of observed data. Parametric models that are suitable for real-world extremes must be flexible -- particularly in their ability to capture asymmetric…
Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. In this paper, we use the concept of sparse regular variation introduced by Meyer and Wintenberger (2021)} to infer the tail…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…