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The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
Quantifying tail dependence is an important issue in insurance and risk management. The prevalent tail dependence coefficient (TDC), however, is known to underestimate the degree of tail dependence and it does not capture non-exchangeable…
Asmussen and Lehtomaa [Distinguishing log-concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function $g$ which is able to distinguish between log-convex and log-concave tail behaviour of distributions, and proposed a…
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…
By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.
Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest…
In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten [12] and Goldie [8] all discount factors in the model are mutually independent. We prove that the tails of the…
We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…
In this paper non-asymptotic exponential estimates are derived for tail of maximum martingale distribution by naturally norming in the spirit of the classical Law of Iterated Logarithm. Key words: Martingales, exponential estimations,…
We study the upper tails for the energy of a randomly charged symmetric and transient random walk. We assume that only charges on the same site interact pairwise. We consider annealed estimates, that is when we average over both randomness,…
We study large deviation properties of probability distributions with either a compact support or a fat tail by comparing them with q-deformed exponential distributions. Our main result is a large deviation property for probability…
Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome but purely technical computations and requires the…
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…
We consider stochastic processes where randomly chosen particles with positive quantities x, y (> 0) interact and exchange the quantities asymmetrically by the rule x' = c{(1-a) x + b y}, y' = d{a x + (1-b) y} (x \ge y), where (0 \le) a, b…
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…
In this paper, asymptotic behavior of convolution of distributions belonging to two subclasses of distributions with exponential tails are considered, respectively. The precise second-order tail asymptotics of the convolutions are derived…
We establish a statistical learning theoretical framework aimed at extrapolation, or out-of-domain generalization, on the unobserved tails of covariates in continuous regression problems. Our strategy involves performing statistical…
It is shown in "SIAM J. Sci. Comput. 39 (2017):B424-B441" that free-form curves used in computer aided geometric design can usually be represented as the solutions of linear differential systems and points and derivatives on the curves can…