Related papers: Measuring the magnitude of sums of independent ran…
Tail dependence plays an essential role in the characterization of joint extreme events in multivariate data. However, most standard tail dependence parameters assume continuous margins. This note presents a form of tail dependence suitable…
We develop a general technique for bounding the tail of the total variation distance between the empirical and the true distributions over countable sets. Our methods sharpen a deviation bound of Devroye (1983) for distributions over finite…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
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.
A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling…
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…
We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
We provide an inequality which is a useful tool in studying both large deviation results and limit theorems for sums of random fields with "negligible" small values. In particular, the inequality covers cases of stable limits for random…
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…
We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical…
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…
We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.
The ratio $P(S_n=x)/P(Z_n=x)$ is investigated for three cases: (a) when $S_n$ is a sum of 1-dependent non-negative integer-valued random variables (rvs), satisfying some moment conditions, and $Z_n$ is Poisson rv; (b) when $S_n$ is a…
We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^2$-distance of quantities related to the characteristic…
A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by…
We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of examples under certain regularity conditions like log-convexity.…
This paper studies the tail probability of weighted sums of the form $\sum_{i=1}^n c_i X_i$, where random variables $X_i$'s are either independent or pairwise quasi-asymptotical independent with heavy tails. Using $h$-insensitive function,…
Estimating the probability of extreme events involving multiple risk factors is a critical challenge in fields such as finance and climate science. This paper proposes a semi-parametric approach to estimate the probability that a…
We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.