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For any nonnegative Borel-measurable function f such that f(x)=0 if and only if x=0, the best constant c_f in the inequality E f(X-E X) \leq c_f E f(X) for all random variables X with a finite mean is obtained.
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Exact bounds on the truncated-tilted mean, with applications, preprint, http://arxiv.org/find/all/1/au:+pinelis/0/1/0/all/0/1
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Exact lower bounds on the exponential moments of Winsorized and truncated random variables
I. Pinelis · 2011
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