Related papers: Generalized Extreme Value distribution parameters …

Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…

The Generalized Extreme Value (GEV) distribution plays a critical role in risk assessment across various domains, such as hydrology, climate science, and finance. In this study, we investigate its application in analyzing intraday trading…

We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…

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…

We notice signatures of extreme events-like behavior in a laser based Ikeda map. The trajectory of the system occasionally travels a large distance away from the bounded chaotic region, which appears as intermittent spiking events in the…

Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…

Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…

This paper presents the design of an extremum seeking controller based on sliding modes and cyclic search for real-time optimization of non-linear multivariable dynamic systems. These systems have arbitrary relative degree, compensated by…

We study the statistical distribution of the closest encounter between observations computed along different trajectories of a mixing dynamical system. At the limit of large trajectories, the distribution is of Gumbel type and depends on…

This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its…

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…

We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of…

Event cameras are an interesting visual exteroceptive sensor that reacts to brightness changes rather than integrating absolute image intensities. Owing to this design, the sensor exhibits strong performance in situations of challenging…

We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…

Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…

Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank-based M-estimator is proposed relying on bivariate margins…

Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…

Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…