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We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One…
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…
In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.
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
In this paper we give an alternative exposition of a recent paper regarding the classification of growth rates of real functions. We take a different point of view, focussing on understanding possible growth rates between polynomial and…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the centered independent ones.
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…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…
We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.
We obtain first decay rates of probabilities of tails of multivariate polynomials built on independent random variables with heavy tails. Then we derive stable limit theorems for nonconventional sums of the form $\sum_{Nt\geq n\geq…
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 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…
In this paper we obtain the non-asymptotic exact moment and tails estimates for polynomial on martingale differences. We give also some examples on order to show the exactness of obtained results.
For dynamical systems modeled by a Young tower with exponential tails, we prove an exponential concentration inequality for all separately Lipschitz observables of n variables. When tails are polynomial, we prove polynomial concentration…