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Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
Speeding has been and continues to be a major contributing factor to traffic fatalities. Various transportation agencies have proposed speed management strategies to reduce the amount of speeding on arterials. While there have been various…
In the recent information-theoretic literature, the concept of extropy has been studied for order statistics. In the present communication we consider a cumulative analogue of extropy in the same vein of cumulative residual (past) entropy…
We review some applications of central limit theorems and extreme values statistics in the context of disordered systems. We discuss several problems, in particular concerning Random Matrix Theory and the generalisation of the Tracy-Widom…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data. We introduce a novel approach to apply extreme value theory to…
We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…
Extremes of information combining inequalities play an important role in the analysis of sparse-graph codes under message-passing decoding. We introduce new tools for the derivation of such inequalities, and show by means of a concrete…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
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…
The Shatters relation and the VC dimension have been investigated since the early seventies. These concepts have found numerous applications in statistics, combinatorics, learning theory and computational geometry. Shattering extremal…
Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…
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…
The statistics of charge transport across a tunnel junction with energy-dependent scattering is investigated. A model with quadratic dispersion relation is discussed in general and, independently, in the two limiting cases of a large…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ball and upperhalfspace.
We quantify the large deviations of Gaussian extreme value statistics on closed convex sets in d-dimensional Euclidean space. The asymptotics imply that the extreme value distribution exhibits a rate function that is a simple quadratic…
This note compares two approaches both alternatively used when establishing normality theorems in univariate Extreme Value Theory. When the underlying distribution function ($df$) is the extremal domain of attraction, it is possible to use…
This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…