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Mathematics > Probability

Title: Halving the bounds for the Markov, Chebyshev, and Chernoff Inequalities using smoothing

Authors: Mark Huber
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 equality. Here we will show that 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 randomness.
Subjects: Probability (math.PR)
MSC classes: 60A05
Cite as: arXiv:1803.06361 [math.PR]
  (or arXiv:1803.06361v1 [math.PR] for this version)

Submission history

From: Mark Huber [view email]
[v1] Fri, 16 Mar 2018 18:19:12 GMT (13kb)