相关论文: On a transformation between distributions obeying …

In this paper, we present several heavy-tailed distributions belonging to the new class J of distributions obeying the principle of a single big jump introduced by Beck et al. [1]. We describe the structure of this class from different…

This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large…

We investigate a new natural class $\mathcal{J}$ of probability distributions modeling large claim sizes, motivated by the `principle of one big jump'. Though significantly more general than the (sub-)class of subexponential distributions…

The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the…

Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing…

We obtain a number of new general properties, related to the closedness of the class of long-tailed distributions under convolutions, that are of interest themselves and may be applied in many models that deal with "plus" and/or "max"…

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…

We introduce a new class of multivariate heavy-tailed distributions that are convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, the multivariate convolution-t distributions embody…

The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…

The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heavy-tailed. Extreme events are large values of the sum and…

It is well-known that large deviations of random walks driven by independent and identically distributed heavy-tailed random variables are governed by the so-called principle of one large jump. We note that further subtleties hold for such…

We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…

We consider questions related to the well-known conjecture due to Embrechts and Goldie on the closedness of different classes of heavy- and light-tailed distributions with respect to convolution roots. We show that the class L(\gamma)\cap…

The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is…

Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed…

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.…

The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…

A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being transient. These distributions are mathematically tractable…

We introduce a new class of heavy-tailed distributions for which any weighted average of independent and identically distributed random variables is larger than one such random variable in (usual) stochastic order. We show that many…

The paper focuses on a class of light-tailed multivariate probability distributions. These are obtained via a transformation of the margins from a heavy-tailed original distribution. This class was introduced in Balkema et al. (J.…