Nonnegativity of odd functional moments of positive random variables with decreasing density
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.
Year of publication: |
1996
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Authors: | Alsmeyer, Gerold |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 26.1996, 1, p. 75-82
|
Publisher: |
Elsevier |
Subject: | Functional moments Skewness Decreasing density |
Saved in:
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