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The Moment Bound Is Tighter Than Chernoff's Bound for Positive Tail Probabilities

Thomas K. Philips and Randolph Nelson
The American Statistician
Vol. 49, No. 2 (May, 1995), pp. 175-178
DOI: 10.2307/2684633
Stable URL: http://www.jstor.org/stable/2684633
Page Count: 4
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The Moment Bound Is Tighter Than Chernoff's Bound for Positive Tail Probabilities
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Abstract

Chernoff's bound on P[X ≥ t] is used almost universally when a tight bound on tail probabilities is required. In this article we show that for all positive t and for all distributions, the moment bound is tighter than Chernoff's bound. By way of example, we demonstrate that the improvement is often substantial.

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