Related papers: Pareto processes for threshold exceedances in spat…
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…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit 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…
When assessing the impact of extreme events, it is often not just a single component, but the combined behaviour of several components which is important. Statistical modelling using multivariate generalized Pareto (GP) distributions…
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…
In many applied fields it is desired to make predictions with the aim of assessing the plausibility of more severe events than those already recorded to safeguard against calamities that have not yet occurred. This problem can be analysed…
Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
Extreme events arising in georeferenced processes can take various forms, such as occurring in isolated patches or stretching contiguously over large areas, and can further vary with the spatial location and the extremeness of the events.…
We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associated to extremal observations of such time series…
In recent years there has been a substantial increase in the availability of datasets which contain information about the location and timing of an event or group of events and the application of methods to analyse spatio-temporal datasets…
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…
An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples of exceedance regions include areas where ozone concentrations exceed safety standards, there is high risk for tornadoes or…
Numerical climate models are complex and combine a large number of physical processes. They are key tools in quantifying the relative contribution of potential anthropogenic causes (e.g., the current increase in greenhouse gases) on high…
In this work we present for the first time an application of the Pareto approach to the modelling of the excesses of galaxy clusters over high-mass thresholds. The distribution of those excesses can be described by the generalized Pareto…
Spatial modelling of extreme values allows studying the risk of joint occurrence of extreme events at different locations and is of significant interest in climatic and other environmental sciences. A popular class of dependence models for…
Max-stable processes are the natural analogues of the generalized extreme-value distribution for the modelling of extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
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…
The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent…