Related papers: Sharp estimates on the tail behavior of a multista…

We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the…

We discuss in this paper a possibility of constructing a whole class of asymptotic distribution-free tests for testing regularly varying tail distributions. The idea is that we treat the tails of distributions as members of a parametric…

Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton…

Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…

The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consider a nonstationary extension where the…

We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag-Leffler type with arbitrary…

The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand…

Proliferating cell populations at steady state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by…

We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of available data is not large, thus the power law asymptotics of the…

Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…

The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some…

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…

In this paper, we propose a method based on GMM (the generalized method of moments) to estimate the parameters of stable distributions with $0<\alpha<2$. We don't assume symmetry for stable distributions.

The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…

Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…

We use characteristic functions to construct alpha(x)-multistable measures and integrals, where the measures behave locally like alpha-stable measures, but with the stability index alpha(x) varying with time x. This enables us to construct…

In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical…

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…

We consider infinitely-wide multi-layer perceptrons (MLPs) which are limits of standard deep feed-forward neural networks. We assume that, for each layer, the weights of an MLP are initialized with i.i.d. samples from either a light-tailed…

The extremes of a univariate Markov chain with regulary varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper, we extend…