Contrast between populations versus spread within populations

Iosif Pinelis

Statistics & Probability Letters, 2017, vol. 121, issue C, 99-100

Abstract: Certain notions of the p-contrast between two populations and the average p-spread within the populations are introduced, where 0⩽p⩽4. It is shown that the p-contrast is no less than the average p-spread for p⩽2—whereas, if the two populations means are the same, then the p-contrast is no greater than the average p-spread for p⩾2. The proof is based on an expression of the absolute moments in terms of the characteristic function. For p=1, extensions of this result to multivariate settings are provided.

Keywords: Probability inequalities; Absolute moments; Characteristic function; p-contrast; p-spread (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2016.10.003

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