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Nonnegativity of odd functional moments of positive random variables with decreasing density

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  • Alsmeyer, Gerold

Abstract

In this note we give some results on the nonnegativity of odd functional moments of random variables with a decreasing density. More precisely, we prove by purely elementary arguments, Egf(X - EX) [greater-or-equal, slanted] 0 for suitable functions gf that satisfy gf(x) = -gf(-x) for all x [greater-or-equal, slanted] 0 and random variables X [greater-or-equal, slanted] 0 with a decreasing Lebesgue density on (0, [infinity]) or counting density on 0. The motivation came from a problem recently published in Statistica Neerlandica (Vol. 43, p. 66). We give a more specialized result in this paper.

Suggested Citation

  • Alsmeyer, Gerold, 1996. "Nonnegativity of odd functional moments of positive random variables with decreasing density," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 75-82, January.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:1:p:75-82
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    References listed on IDEAS

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    1. Bélisle, Claude, 1991. "Odd central moments of unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 97-107, August.
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    Cited by:

    1. Kim, Byungwon & Schulz, Jörn & Jung, Sungkyu, 2020. "Kurtosis test of modality for rotationally symmetric distributions on hyperspheres," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    2. Alsmeyer, Gerold & Rösler, Uwe, 2003. "The best constant in the Topchii-Vatutin inequality for martingales," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 199-206, November.

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