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Abstract In this paper, we present a refinement of Hoeffding's inequality which is of closed form and which significantly improves on this inequality in many cases. Some numerical comparisons are also presented. Keywords: Hoeffding's inequalityarithmetic mean–geometric mean inequalitymoment-generating function AMS Subject Classifications : 60E1562E17 Acknowledgements The authors thank the referee whose comments helped to improve this paper. In particular, the comments allowed us to generate a more streamlined proof of Theorem 1.3.
From et al. (2011) studied this question.