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A Generalization of Levy's Concentration-Variance Inequality
Probability Theory and Related Fields
  • R. D. Foley, Georgia Institute of Technology - Main Campus
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
  • M. C. Spruill, Georgia Institute of Technology - Main Campus
Publication Date
3-1-1990
Abstract

Sharp lower bounds are found for the concentration of a probability distribution as a function of the expectation of any given convex symmetric function φ. In the case φ(x)=(x-c)2, where c is the expected value of the distribution, these bounds yield the classical concentration-variance inequality of Lévy. An analogous sharp inequality is obtained in a similar linear search setting, where a sharp lower bound for the concentration is found as a function of the maximum probability swept out from a fixed starting point by a path of given length.

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Citation Information
R. D. Foley, Theodore P. Hill and M. C. Spruill. "A Generalization of Levy's Concentration-Variance Inequality" Probability Theory and Related Fields Vol. 86 Iss. 1 (1990) p. 53 - 62
Available at: http://works.bepress.com/tphill/18/