Related papers: Probabilities for asymmetric p-outside values
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
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…
We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…
We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that if the random walk is…
The statistical distribution of the ratio of two normal random variables is characterized by its heavy-tailed nature and absence of finite moments. The shape of its density function is highly variable, capable of exhibiting unimodal or…
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…
Understanding multivariate dependencies in both the bulk and the tails of a distribution is an important problem for many applications, such as ensuring algorithms are robust to observations that are infrequent but have devastating effects.…
The extremal tail probabilities of moving sums in a marked Poisson random field is examined here. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. Change of measure…
This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Levy property. We then give a connection…
We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which…
A new three-parameter cumulative distribution function defined on $(\alpha,\infty)$, for some $\alpha\geq0$, with asymmetric probability density function and showing exponential decays at its both tails, is introduced. The new distribution…
Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…
Assessing and managing risks in a changing climate requires projections that account for decision-relevant uncertainties. These deep uncertainties are often approximated by ensembles of Earth-system model runs that sample only a subset of…
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…
The box-and-whisker plot, introduced by Tukey (1977), is one of the most popular graphical methods in descriptive statistics. On the other hand, however, Tukey's boxplot is free of sample size, yielding the so-called "one-size-fits-all"…
In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…
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…
In this article two methods to distinguish between polynomial and exponential tails are introduced. The methods are mainly based on the properties of the residual coefficient of variation for the exponential and non-exponential…
In traditional extreme value analysis, the bulk of the data is ignored, and only the tails of the distribution are used for inference. Extreme observations are specified as values that exceed a threshold or as maximum values over distinct…
This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito…