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We consider the sums $S_n=\xi_1+\cdots+\xi_n$ of independent identically distributed random variables. We do not assume that the $\xi$'s have a finite mean. Under subexponential type conditions on distribution of the summands, we find the…

Probability · Mathematics 2013-03-20 D. Denisov , S. Foss , D. Korshunov

In this paper we propose a model with a Dirichlet process mixture of gamma densities in the bulk part below threshold and a generalized Pareto density in the tail for extreme value estimation. The proposed model is simple and flexible…

Machine Learning · Statistics 2013-04-03 Jairo Fuquene

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…

Risk Management · Quantitative Finance 2016-04-12 Oliver Kley , Claudia Kluppelberg

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…

Machine Learning · Statistics 2026-05-05 Sebastian Engelke , Nicola Gnecco , Anne Sabourin

In survival analysis, the estimation of the proportion of subjects who will never experience the event of interest, termed the cure rate, has received considerable attention recently. Its estimation can be a particularly difficult task when…

Statistics Theory · Mathematics 2025-04-02 Jan Beirlant , Martin Bladt , Ingrid Van Keilegom

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…

Statistics Theory · Mathematics 2018-12-20 Jingjing Zou , Richard A. Davis , Gennady Samorodnitsky

A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…

Statistics Theory · Mathematics 2019-12-09 Benjamin Bobbia , Clément Dombry , Davit Varron

The behavior of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for…

Methodology · Statistics 2025-03-11 Sebastian Engelke , Nicola Gnecco , Frank Röttger

We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account…

Risk Management · Quantitative Finance 2019-02-11 Oliver Kley , Claudia Klüppelberg , Sandra Paterlini

We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of…

Probability · Mathematics 2009-06-29 Abhimanyu Mitra , Sidney I. Resnick

In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance…

Statistics Theory · Mathematics 2020-09-29 Jose Carlos Araujo Acuna , Hansjoerg Albrecher , Jan Beirlant

Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…

Methodology · Statistics 2024-05-06 Reetam Majumder , Brian J. Reich , Benjamin A. Shaby

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…

Methodology · Statistics 2023-12-18 Liujun Chen , Deyuan Li , Chen Zhou

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…

Methodology · Statistics 2026-02-11 Lorenzo Dell'Oro , Carlo Gaetan , Thomas Opitz

The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…

Statistics Theory · Mathematics 2019-07-23 Holger Drees , Miran Knezevic

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

Probability · Mathematics 2015-09-03 Helena Ferreira , Luísa Pereira , Ana Paula Martins

Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…

Statistics Theory · Mathematics 2017-08-08 Clement Dombry , Sebastian Engelke , Marco Oesting

Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used…

Methodology · Statistics 2022-12-22 Jasper Velthoen , Clément Dombry , Juan-Juan Cai , Sebastian Engelke

Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…

Methodology · Statistics 2025-08-05 Myungsoo Yoo , Likun Zhang , Christopher K. Wikle , Thomas Opitz

This article is written for pedagogical purposes aiming at practitioners trying to estimate the finite support of continuous probability distributions, i.e., the minimum and the maximum of a distribution defined on a finite domain.…

Machine Learning · Computer Science 2023-03-23 Masataro Asai