Summary
For a non-negative random variable X and α≧1 such that EX<∞, E(X-Y) +α /{E(X-y) +}+ is monotonic-decreasing in y, and hence no smaller than EX α. Inequalities for E(X-Y) α+ E(α, β≧1, y, z≧0) are also given. This relation enables an inequality of Kingman for the mean waiting time in a stationary GI/G/1 queue to be sharpened.
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Work done as Visiting Fellow, Department of Statistics, University of Melbourne
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Daley, D.J. Inequalities for moments of tails of random variables, with a queueing application. Z. Wahrscheinlichkeitstheorie verw Gebiete 41, 139–143 (1977). https://doi.org/10.1007/BF00538417
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DOI: https://doi.org/10.1007/BF00538417