Related papers: Lower limits for distributions of randomly stopped…
The approach used by Kalashnikov and Tsitsiashvili for constructing upper bounds for the tail distribution of a geometric sum with subexponential summands is reconsidered. By expressing the problem in a more probabilistic light, several…
We provide a necessary and sufficient condition for the ratio of two jointly alpha-Frechet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution and is easy to check in…
We demonstrate that the tail of transmission distribution through 1D disordered Anderson chain is a strong function of the correlation radius of the random potential, $a$, even when this radius is much shorter than the de Broglie…
We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Levy property. We then give a connection…
We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which…
This note studies the asymptotic properties of the variable $$Z_d:=\frac{X_1}{d}|\{X_1+X_2=d\},$$ as $d\to \infty$. Here $X_1$ and $X_2$ are non-negative i.i.d. variables with a common twice differentiable density function $f$. General…
We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…
In this paper, we give a Breiman's theorem for conditional dependent random vector, where one component has a regularly-varying-tailed distribution with the index $\alpha\ge0$ and its slowly varying function satisfies a relaxed condition,…
This paper investigates the decay rate of the probability that the row sum of a triangular array of truncated heavy tailed random variables is larger than an integer (k) times the truncating threshold, as both - the number of summands and…
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…
Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in…
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.
We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and find the sharp constant for such stochastic domination.
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables, and $\eta$ be a counting random variable independent of this sequence. We consider conditions for $\{\xi_1,\xi_2,\ldots\}$ and $\eta$ under which the distribution…
Consider a probability distribution subordinate to a subexponential distribution with finite mean. In this paper, we discuss the second order tail behavior of the subordinated distribution within a rather general framework in which we do…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
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…
We consider certain Fibonacci-like sequences $(X_n)_{n\geq 0}$ perturbed with a random noise. Our main result is that $\frac{1}{X_n}\sum_{k=0}^{n-1}X_k$ converges in distribution, as $n$ goes to infinity, to a random variable $W$ with…