Inequalities relating maximal moments to other measures of dispersion |
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Authors: | P C Allaart |
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Institution: | Mathematics Department, University of North Texas, USA |
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Abstract: | Let X , X 1, ..., Xk be i.i.d. random variables, and for k ∈ N let Dk ( X ) = E ( X 1 V ... V 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 Lévy concentration Ql ( X ) = sup x ∈ R P ( X ∈ x , x + l ]). This inequality, which is analogous to P. Levy'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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Keywords: | expected maximum of an i i d random sample Levy concentration measure of dispersion |
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