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Since the extreme value index (EVI) controls the tail behaviour of the distribution function, the estimation of EVI is a very important topic in extreme value theory. Recent developments in the estimation of EVI along with covariates have…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme…
Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by…
This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and…
A proper channel modeling methodology that characterizes the statistics of extreme events is key in the design of a system at an ultra-reliable regime of operation. The strict constraint of ultra-reliability corresponds to the packet error…
In most risk assessment studies, it is important to accurately capture the entire distribution of the multivariate random vector of interest from low to high values. For example, in climate sciences, low precipitation events may lead to…
Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction…
Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed in the…
Adaptation-relevant predictions of climate change are often derived by combining climate model simulations in a multi-model ensemble. Model evaluation methods used in performance-based ensemble weighting schemes have limitations in the…
The extreme value index (EVI) characterizes the tail behavior of a distribution and is crucial for extreme value theory. Inference on the EVI is challenging due to data scarcity in the tail region. We propose a novel method for constructing…
Extreme value theory (EVT) provides an elegant mathematical tool for the statistical analysis of rare events. When data are collected from multiple population subgroups, because some subgroups may have less data available for extreme value…
Extreme value analysis in the presence of censoring is receiving much attention as it has applications in many disciplines, including survival and reliability studies. Estimation of extreme value index (EVI) is of primary importance as it…
Impact assessment of natural hazards requires the consideration of both extreme and non-extreme events. Extensive research has been conducted on the joint modeling of bulk and tail in univariate settings; however, the corresponding body of…
Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…
The block maximum method, which is widely used in extreme value analysis, uses a generalized extreme value distribution to approximate that of the maximum of m observations. The quality of this approximation depends on the value of m and…
A major issue of extreme value analysis is the determination of the shape parameter $\xi$ common to Generalized Extreme Value (GEV) and Generalized Pareto (GP) distributions, which drives the tail behavior, and is of major impact on the…
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…
This paper deals with parameter estimation from extreme measurements. While being a special case of parameter estimation from partial data, in scenarios where only one sample from a given set of K measurements can be extracted, choosing…
In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not…
The estimation of the Extreme Value Index (EVI) is fundamental in extreme value analysis but suffers from high variance due to reliance on only a few extreme observations. We propose a control variates based transfer learning approach in a…