Related papers: Multivariate tail covariance for generalized skew-…
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…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
After having closely re-examined the notion of a L\'evy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. A multivariate extension was established by Aulbach et al.…
A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the split-t (AST) distribution. With…
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…
For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present…
Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
In this article we study the tail probability of the mass of critical Gaussian multiplicative chaos (GMC) associated to a general class of log-correlated Gaussian fields in any dimension, including the Gaussian free field (GFF) in dimension…
We consider heavy-tailed distributions and compare the well-known estimators of the tail index, based on extreme value theory with a comparatively recent estimator based on a different idea.
In this note, we investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parametrizations and…
The Weibull tail-coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull-type tails. Several distributions, such as normal, Gamma, Weibull, and Logistic distributions, exhibit this type of tail…
Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…
In this work, we establish some stochastic comparison results for multivariate skew-elliptical random vectors. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings as well as many of their special…
We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent…
This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we…