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Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 2, Pages 397–403 (Mi tvp2424)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Lower Bounds for Tails of Sums of Independent Symmetric Random Variables

L. Mattner

University Lübeck

Abstract: The approach of Kleitman [Adv. in Math., 5 (1970), pp. 155–157] and Kanter [J. Multivariate Anal., 6 (1976), pp. 222–236] 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 [Theory Probab. Appl., 46 (2002), pp. 728–735], and complements the comparison theorems of Birnbaum [Ann. Math. Statist., 19 (1948), pp. 76–81] and Pruss [Ann. Inst. H. Poincaré, 33 (1997), pp. 651–671]). Birnbaum's theorem for unimodal random variables is extended to the lattice case.

Keywords: Bernoulli convolution, concentration function, deviation probabilities, Poisson binomial distribution, symmetric three point convolution, unimodality.

DOI: https://doi.org/10.4213/tvp2424

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English version:
Theory of Probability and its Applications, 2009, 53:2, 334–339

Bibliographic databases:

Received: 07.09.2006
Language: English

Citation: L. Mattner, “Lower Bounds for Tails of Sums of Independent Symmetric Random Variables”, Teor. Veroyatnost. i Primenen., 53:2 (2008), 397–403; Theory Probab. Appl., 53:2 (2009), 334–339

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    This publication is cited in the following articles:
    1. S. V. Astashkin, K. E. Tikhomirov, “On Probability Analogs of Rosenthal's Inequality”, Math. Notes, 90:5 (2011), 644–650  mathnet  crossref  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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