Related papers: Averaging of random variables and fields

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…

We derive the sharp non-asymptotical uniform estimations for tails of distributions for classical normed sums of centered normed independent random vectors having a moderate decreasing individual tails of summands.

In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically…

The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…

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 obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…

We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials

We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…

Let F be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F.…

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$,…

We consider the tail behavior of random variables $R$ which are solutions of the distributional equation $R\stackrel{d}{=}Q+MR$, where $(Q,M)$ is independent of $R$ and $|M|\le 1$. Goldie and Gr\"{u}bel showed that the tails of $R$ are no…

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of…

Tail averaging consists in averaging the last examples in a stream. Common techniques either have a memory requirement which grows with the number of samples to average, are not available at every timestep or do not accomodate growing…

We estimate up to universal constants tails of symmetric and totally asymmetric 1-dimensional $\alpha$-stable distributions in terms of functions of the parameters of these distributions. In particular, for values of $\alpha$ close to $2$…

For a distribution $F^{*\tau}$ of a random sum $S_{\tau}=\xi_1+...+\xi_{\tau}$ of i.i.d. random variables with a common distribution $F$ on the half-line $[0,\infty)$, we study the limits of the ratios of tails…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…

This article studies the convergence rate of the sample mean for $\varphi$-mixing dependent random variables with finite means and infinite variances. Dividing the sample mean into sum of the average of the main parts and the average of the…

We derive the tail inequalities between two random variables starting from inequalities between its moment, or more generally between its Lebesgue-Riesz norms, which holds true on certain sets of parameters. We consider some applications…

We consider the random variables $R$ which are solutions of the distributional equation $R\overset{\cL}{=}MR+Q$, where $(Q,M)$ is independent of $R$ and $\ABS{M}\leq 1$. Goldie and Gr\"ubel showed that the tails of $R$ are no heavier than…

The objective of this paper is to extend an estimation method of parameters of the stable distributions in $\rd$ to the regularly varying tails distributions in an arbitrary cone. The consistency and the asymptotic normality of estimators…