Related papers: Only Segmented Heavy Tails Can Produce a Light-Tai…

Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…

We give conditions under which the tail probability of the supremum over unit interval of a Levy process with light tail is equivalent to the tail of the value of the process at the right endpoint.

We investigate a way of comparing and classifying tails of random variables. Our approach extends the notion of classical indices, such as exponential and moment indices, which are widely used measuring heaviness of tail functions. A…

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly…

In a seminal paper Biggins and Kyprianou \cite{BKy04} proved the existence of a non degenerate limit for the {\it Derivative martingale} of the branching random walk. As shown in \cite{Aid11} and \cite{Mad11}, this is an object of central…

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…

Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…

We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.

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…

We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…

The total number of fatalities of an epidemic outbreak is a dramatic but extremely informative quantity. Knowledge of the statistics of this quantity allows the calculation of the mean total number of fatalities conditioned to the fact that…

Let $\{X_i\}_{i\geq1}$ be an i.i.d. sequence of random variables and define, for $n\geq2$, \[T_n=\cases{n^{-1/2}\hat{\sigma}_n^{-1}S_n,\quad \hat{\sigma}_n>0,\cr 0,\quad \hat{\sigma}_n=0,}with S_n=\sum_{i=1}^nX_i,…

Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the…

We analyze systems of agents sharing light-tailed risky claims issued by different financial objects. Assuming exponentially distributed claims, we obtain that both agents' and system's losses follow generalized exponential mixture…

Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…

Let $(X_n:n\geq 0)$ be a sequence of i.i.d. r.v.'s with negative mean. Set $S_0=0$ and define $S_n=X_1+... +X_n$. We propose an importance sampling algorithm to estimate the tail of $M=\max \{S_n:n\geq 0\}$ that is strongly efficient for…

The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if $\hat{\alpha}_n$ is an…

We say that a random variable is $light$-$tailed$ if moments of order $2+\epsilon$ are finite for some $\epsilon>0$; otherwise, we say that it is $heavy$-$tailed$. We study queueing networks that operate under the Max-Weight scheduling…

We study conditions under which $P(S_\tau>x)\sim P(M_\tau>x)\sim E\tau P(\xi_1>x)$ as $x\to\infty$, where $S_\tau$ is a sum $\xi_1+...+\xi_\tau$ of random size $\tau$ and $M_\tau$ is a maximum of partial sums $M_\tau=\max_{n\le\tau}S_n$.…

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…