Lower bounds for tails of sums of independent symmetric random variables

Details Lower bounds for tails of sums of independent symmetric random variables Lower bounds for tails of sums of independent symmetric random variables

2006-09-07

arxiv.org/abs/math/0609200v1

Mathematics

Probability

7 pages

Scientific paper

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.

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