# Halving the Bounds for the Markov, Chebyshev, and Chernoff Inequalities Using Smoothing

@article{Huber2019HalvingTB, title={Halving the Bounds for the Markov, Chebyshev, and Chernoff Inequalities Using Smoothing}, author={Mark Huber}, journal={The American Mathematical Monthly}, year={2019}, volume={126}, pages={915 - 927} }

Abstract The Markov, Chebyshev, and Chernoff inequalities are some of the most widely used methods for bounding the tail probabilities of random variables. In all three cases, the bounds are tight in the sense that there exists easy examples where the inequalities become equalities. Here we will show, through a simple smoothing using auxiliary randomness, that each of the three bounds can be cut in half. In many common cases, the halving can be achieved without the need for the auxiliary… CONTINUE READING

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##### Publications referenced by this paper.

SHOWING 1-10 OF 18 REFERENCES

## On Complexity of Counting

VIEW 2 EXCERPTS

## A First Course in Probability

VIEW 1 EXCERPT

## A Career in Statistics

VIEW 1 EXCERPT