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Probability inequalities for convex sets and multidimensional concentration functions

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  • Kanter, Marek

Abstract

This paper derives a sharp bound for the probability that a sum of independent symmetric random vectors lies in a symmetric convex set. In one dimension this bound is an improvement of an inequality first proved by Kolmogorov. The subject of multidimensional concentration functions is also treated.

Suggested Citation

  • Kanter, Marek, 1976. "Probability inequalities for convex sets and multidimensional concentration functions," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 222-236, June.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:2:p:222-236
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    Cited by:

    1. Mattner, Lutz & Roos, Bero, 2008. "Maximal probabilities of convolution powers of discrete uniform distributions," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2992-2996, December.

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