In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lataa la on bounds on moments of such sums. We also give a new proof of Lataa la's result for nonnegative random variables, and improve one of the constants in his inequality.

Assuming absolute continuity of marginals, we give the distribution for sums of dependent random variables from some class of Archimedean copulas and the marginal distribution functions of all order statistics.We use conditional independence structure of random variables from this class of Archimedean copulas and Laplace transform. Additionally, we present an application of our results to VaR e...

In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.

This paper obtains some asymptotics for the tail probabilities of the maximum of sums and random sums of negatively associated (NA) random variables with heavy tails, showing that the NA dependence structure does not affect the asymptotic behavior of these tail probabilities. r 2004 Elsevier B.V. All rights reserved.

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lyingwithin a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at z...

In this review, we consider boundary problems for random walks generated by sums of independent items and some of their generalizations. Let 1, 42, . . * be identically distributed independent random variables with distribution frunction F(x). Let S = 0, Sn = Sk= Ok with n = 1, 2, * -. We shall study the properties of the random trajectory formed by the sums S0, S1, 82, . Let n be an integer pa...

We present a general transfer theorem for random sequences with independent random indexes in the double array limit setting. We also prove its partial inverse providing necessary and sufficient conditions for the convergence of randomly indexed random sequences. Special attention is paid to the cases of random sums of independent not necessarily identically distributed random variables and sta...