Related papers: Large deviation estimates involving deformed expon…

To account quantitatively for many reported ``natural'' fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which…

We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test…

This paper is organized in three parts closely related to closure properties of heavy-tailed distributions and heavy-tailed random vectors. In the first part we consider two random variables X and Y with distributions F and G respectively.…

We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large…

In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…

We obtain sample-path large deviations for a class of one-dimensional stochastic differential equations with bounded drifts and heavy-tailed L\'evy processes. These heavy-tailed L\'evy processes do not satisfy the exponential integrability…

In this paper, according to a certain criterion, we divide the exponential distribution class into three subclasses. One of them is closely related to the regular-variation-tailed distribution class, so it is called the…

The tail index, indicating the degree of fatness of the tail distribution, is an important component of extreme value theory since it dominates the asymptotic distribution of extreme values such as the sample maximum. In this paper, we…

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex…

Applying a modification of Extreme value Theory (thanks to a dual distribution technique by the authors on data over the past 2,500 years, we show that pandemics are extremely fat-tailed in terms of fatalities, with a marked potentially…

Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…

We propose a distance supervised relation extraction approach for long-tailed, imbalanced data which is prevalent in real-world settings. Here, the challenge is to learn accurate "few-shot" models for classes existing at the tail of the…

We consider a model for multivariate data with heavy-tailed marginal distributions and a Gaussian dependence structure. The different marginals in the model are allowed to have non-identical tail behavior in contrast to most popular…

The theory of Extreme Physical Information (EPI) is used to deduce a probability density function (PDF) of a system that exhibits a power law tail. The computed PDF is useful to study and fit several observed distributions in complex…

The class of subweibull distributions has recently been shown to generalize the important properties of subexponential and subgaussian random variables. We describe alternative characterizations of subweibull distributions and detail the…

We provide bounds on the tail probabilities for simple procedures that generate random samples _without replacement_, when the probabilities of being selected need not be equal.

We provide exact large-time equivalents of the density and upper tail distributions of the exponential functional of a subordinator in terms of its Laplace exponents. This improves previous results on the logarithmic asymptotic behaviour of…

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…

We obtain concentration and large deviation for the sums of independent and identically distributed random variables with heavy-tailed distributions. Our concentration results are concerned with random variables whose distributions satisfy…

The solution of $ X=AX+1 $ is analyzed for a discrete variable $ A $ with $ \mathbb{P}\left[A=0\right]>0 $. Accordingly, a fast algorithm is presented to calculate the obtained heavy tail density. To exemplify, the compound product…