Related papers: Orthogonal parametrisations of Extreme-Value distr…
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 classical approach to multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction. This requires each marginal distribution be individually attracted to a univariate extreme…
Count data are omnipresent in many applied fields, often with overdispersion due to an excess of zeroes or extreme values. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on the…
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 maximum product of spacings (MPS) is employed in the estimation of the Generalized Extreme Value Distribution (GEV) and the Generalized Pareto Distribution (GPD). Efficient estimators are obtained by the MPS for all $\gamma$. This…
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…
Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…
From environmental sciences to finance, there is a growing demand for methods that can assess the risks of extreme events beyond those observed in available data. Extrapolating extreme events beyond the range of the data is not obvious.…
This paper investigates the use of extreme value theory for modelling the distribution of demand-net-of-wind for capacity adequacy assessment. Extreme value theory approaches are well-established and mathematically justified methods for…
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…
In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
One of the main goal of extreme value analysis is to estimate the probability of rare events given a sample from an unknown distribution. The upper tail behavior of this distribution is described by the extreme value index. We present a new…
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…
A method is described for predicting extremes values beyond the span of historical data. The method - based on extending a curve fitted to a location- and scale-invariant variation of the double-logarithmic QQ-plot - is simple and…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
Recently attention has been drawn to practical problems with the use of unbounded Pareto distributions, for instance when there are natural upper bounds that truncate the probability tail. Aban, Meerschaert and Panorska (2006) derived the…