Related papers: On discrete approximations of stable distributions

Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…

We investigate the application of the Adaptive Multilevel Splitting algorithm for the estimation of tail probabilities of solutions of Stochastic Differential Equations evaluated at a given time, and of associated temporal averages. We…

The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this…

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical…

The explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying theory of regular variation, without appeal to the general…

We propose a simple way of testing whether a given set of observations can come from a given theoretical cumulative distribution. In the test more weight is attached to the tails of the distribution than in the usual Kolmogorov or Smirnov…

The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…

In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals…

This paper studies the distributed optimization problem under the influence of heavy-tailed gradient noises. Here, a heavy-tailed noise means that the noise does not necessarily satisfy the bounded variance assumption. Instead, it satisfies…

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

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…

Statistical modeling of high dimensional extremes remains challenging and has generally been limited to moderate dimensions. Understanding structural relationships among variables at their extreme levels is crucial both for constructing…

In this paper, we investigate and develop a new approach to the numerical analysis and characterization of random fluctuations with heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare…

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 study a scalable alternative to robust gradient descent (RGD) techniques that can be used when the gradients can be heavy-tailed, though this will be unknown to the learner. The core technique is simple: instead of trying to robustly…

This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation…

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…