Related papers: Limit theorems for sums of random variables with m…
We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft…
In this paper we revisited the classical problem of max-sum equivalence of randomly weighted sums in two dimensions. In opposite to the most papers in literature, we consider that there exists some interdependence between the primary random…
Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…
The sums and maxima of weighted non-stationary random length sequences of regularly varying random variables may have the same tail and extremal indices, Markovich and Rodionov (2020). The main constraints are that there exists a unique…
We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…
In this paper, we obtain some results on precise large deviations for non-random and random sums of widely dependent random variables with common dominatedly varying tail distribution or consistently varying tail distribution on…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
The contribution of this paper is to introduce change of measure based techniques for the rare-event analysis of heavy-tailed stochastic processes. Our changes-of-measure are parameterized by a family of distributions admitting a mixture…
In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We…
In this paper we introduce and study several multivariate, heavy-tailed distribution classes, and we explore their closure properties and their applications. We consider the class of multivariate, positively decreasing distributions, and…
We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…
The paper focuses on a class of light-tailed multivariate probability distributions. These are obtained via a transformation of the margins from a heavy-tailed original distribution. This class was introduced in Balkema et al. (J.…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
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…
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…
We give explicit bounds for the tail probabilities for sums of independent geometric or exponential variables, possibly with different parameters.
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
We study the probability distribution $P$ of the sum of a large number of non-identically distributed random variables $n_m$. Condensation of fluctuations, the phenomenon whereby one of such variables provides a macroscopic contribution to…
This article deals with the hypothesis test for the extremely heavy-tailed distributions with infinite mean or variance by using a truncated sample mean. We obtain three necessary and sufficient conditions under which the asymptotic…