%0 Journal Article
%T Lower bounds for tails of sums of independent symmetric random variables
%A Lutz Mattner
%J Mathematics
%D 2006
%I arXiv
%X The approach of Kleitman (1970) and Kanter (1976) to multivariate concentration function inequalities is generalized in order to obtain for deviation probabilities of sums of independent symmetric random variables a lower bound depending only on deviation probabilities of the terms of the sum. This bound is optimal up to discretization effects, improves on a result of Nagaev (2001), and complements the comparison theorems of Birnbaum (1948) and Pruss (1997). Birnbaum's theorem for unimodal random variables is extended to the lattice case.
%U http://arxiv.org/abs/math/0609200v1