Title

Contrast between populations versus spread within populations

Document Type

Article

Publication Date

2-1-2017

Abstract

© 2016 Elsevier B.V. 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.

Publication Title

Statistics and Probability Letters

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