Related papers: Multivariate generalized Pareto distributions alon…
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…
We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…
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…
Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…
A method is described for predicting extremes values beyond the span of historical data. The method - based on extending a curve fitted to a location- and scale-invariant variation of the double-logarithmic QQ-plot - is simple and…
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…
Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of…
This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for…
In this paper we obtain closed expressions for the probability distribution function, when we consider aggregated risks with multivariate dependent Pareto distributions. We work with the dependent multivariate Pareto type II proposed by…
Designs conditions for marine structures are typically informed by threshold-based extreme value analyses of oceanographic variables, in which excesses of a high threshold are modelled by a generalized Pareto (GP) distribution. Too low a…
Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…
In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the…
In order to describe the extremal behaviour of some stochastic process $X$, approaches from univariate extreme value theory are typically generalized to the spatial domain. In particular, generalized peaks-over-threshold approaches allow…
We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…
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 a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
In risk analysis, the mean excess plot is a commonly used exploratory plotting technique for confirming iid data is consistent with a generalized Pareto assumption for the underlying distribution, since in the presence of such a…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…