Bounding Probability of Small Deviation: A Fourth Moment Approach

  title={Bounding Probability of Small Deviation: A Fourth Moment Approach},
  author={Simai He and Jiawei Zhang and Shuzhong Zhang},
  journal={Math. Oper. Res.},
In this paper we study the problem of upper bounding the probability that a random variable is above its expected value by a small amount (relative to the expected value), by means of the second and the fourth (central) moments of the random variable. In this particular context, many classical inequalities yield only trivial bounds. We obtain tight upper bounds by studying the primal-dual moments-generating conic optimization problems. As an application, we demonstrate that given the new… 
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