Inequalities Relating Maximal Moments to Other Measures of Dispersion
نویسنده
چکیده
Let X; X 1 ; : : : ; X k be i.i.d. random variables, and for k 2 IN let D k (X) = E(X 1 _ _ X k+1) ? EX be the k-th centralized maximal moment. A sharp lower bound is given for D 1 (X) in terms of the L evy concentration Q l (X) = sup x2IR P (X 2 x; x + l]). This inequality, which is analogous to P. L evy's concentration-variance inequality, illustrates the fact that maximal moments are a gauge of how much spread out the underlying distribution is. It is also shown that the centralized maximal moments are increased under convolution.
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