Related papers: Extreme value and record statistics in heavy-taile…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
In this paper we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree…
Several theoretical results concerning event-by-event fluctuations are discussed: (1) a role of the global conservation laws and concept of statistical ensembles; (2) strongly intensive measures are introduced; they give a possibility to…
In this paper we prove the existence of Extreme Value Laws for dynamical systems perturbed by instrument-like-error, also called observational noise. An orbit perturbed with observational noise mimics the behavior of an instrumentally…
We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of…
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
Spatiotemporal complexity is induced in a two dimensional nonlinear disordered lattice through the modulational instability of an initially weakly perturbed excitation. In the course of evolution we observe the formation of transient as…
Recent experiments have shown that stochastic effects exerted at the level of translation contribute a substantial portion of the variation in abundance of proteins expressed at moderate to high levels. This study analyzes translational…
We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail…
This paper focuses on rare events associated with the tail probabilities of the extremal eigenvalues in the $\beta$-Jacobi ensemble, which plays a critical role in both multivariate statistical analysis and statistical physics. Under the…
The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often…
Temporal sequences of discrete events that describe natural and social processes are often driven by non-Poisson dynamics. In addition to a heavy-tailed interevent time distribution, which primarily captures the deviation from a Poisson…
Extreme precipitation shows non-stationary behavior over time, but also with respect to other large-scale variables. While this effect is often neglected, we propose a model including the influence of North Atlantic Oscillation, time,…
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
Extreme events generated by complex systems have been intensively studied in many fields due to their great impact on scientific research and our daily lives. However, their prediction is still a challenge in spite of the tremendous…
We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is…
We address the estimation of quantiles from heavy-tailed distributions when functional covariate information is available and in the case where the order of the quantile converges to one as the sample size increases. Such "extreme"…
We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in…
As a useful and elegant tool of extreme value theory, the study of point processes on a metric space is important and necessary for the analyses of heavy-tailed functional data. This paper focuses on the definition and properties of such…