Related papers: Asymptotic theory for extreme value generalized ad…
The generalized Pareto distribution (GPD) is a fundamental model for analyzing the tail behavior of a distribution. In particular, the shape parameter of the GPD characterizes the extremal properties of the distribution. As described in…
The Generalized Pareto Distribution (GPD) plays a central role in modelling heavy tail phenomena in many applications. Applying the GPD to actual datasets however is a non-trivial task. One common way suggested in the literature to…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
This article extends the multivariate extreme value theory (MEVT) to discrete settings, focusing on the generalized Pareto distribution (GPD) as a foundational tool. The purpose of the study is to enhance the understanding of extreme…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
This paper reviews generalized Pareto copulas (GPC), which turn out to be a key to multivariate extreme value theory. Any GPC can be represented in an easy analytic way using a particular type of norm on $\mathbb{R}^d$, called $D$-norm. The…
The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analyzing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed…
This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
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…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
The statistical modeling of discrete extremes has received less attention than their continuous counterparts in the Extreme Value Theory (EVT) literature. One approach to the transition from continuous to discrete extremes is the modeling…
Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of…
When assessing the impact of extreme events, it is often not just a single component, but the combined behaviour of several components which is important. Statistical modelling using multivariate generalized Pareto (GP) distributions…
In this short note, I comment on the research of Pisarenko et al. (2014) regarding the extreme value theory and statistics in case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic…
This article introduces the R package evgam. The package provides functions for fitting extreme value distributions. These include the generalized extreme value and generalized Pareto distributions. The former can also be fitted through a…
For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the…
In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the…
The Extended Generalized Pareto Distribution (EGPD) (Naveau et al. 2016) is a family of distribution that has been introduced to model the full range of a positive random variable but with the lower and the upper tails distributed according…