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We derive the sharp non-asymptotical uniform estimations for tails of distributions for classical normed sums of centered normed independent random vectors having a moderate decreasing individual tails of summands.
We examine random variables in the power law/regularly varying class with stochastic tail exponent, the exponent $\alpha$ having its own distribution. We show the effect of stochasticity of $\alpha$ on the expectation and higher moments of…
We construct a two-tailed peak-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating…
We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
Tail Gini functional is a measure of tail risk variability for systemic risks, and has many applications in banking, finance and insurance. Meanwhile, there is growing attention on aymptotic independent pairs in quantitative risk…
We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
Sub-Gaussian estimates for the natural random walk is typical of many regular fractal graphs. Subordination shows that there exist heavy tailed jump processes whose jump indices are greater than or equal to two. However, the existing…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
Rare events, and more general risk-sensitive quantities-of-interest (QoIs), are significantly impacted by uncertainty in the tail behavior of a distribution. Uncertainty in the tail can take many different forms, each of which leads to a…
A common bottleneck in evaluating extremal performance measures is that, due to their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric…
Topological Data Analysis (TDA) refers to an approach that uses concepts from algebraic topology to study the "shapes" of datasets. The main focus of this paper is persistent homology, a ubiquitous tool in TDA. Basing our study on this, we…
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 general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…
In many areas of interest, modern risk assessment requires estimation of the extremal behaviour of sums of random variables. We derive the first order upper-tail behaviour of the weighted sum of bivariate random variables under weak…
We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…
The purpose of this paper is to show that the use of heavy-tailed distributions in Financial problems is theoretically baseless and can lead to significant misunderstandings. The reason for this the authors see in an incorrect…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…