The sum of a random number independent and identically distributed vectors has distribution which is not analytically tractable, in the general case. problem been addressed by means asymptotic approximations embedding summands stochastically increasing sequence. Another approach relies on fitting flexible tractable parametric, multivariate distributions, as for example finite mixtures. Both app...

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that...

Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of global quantities, in a direct or indirect way. This review discusses differe...

We use and extend a method by Hoeffding to obtain strong large deviation bounds for sums of dependent random variables with suitable dependency structure. The method is based on breaking up the sum into sums of independent variables. Applications are given to U -statistics, random strings and random graphs.