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

Gerold Alsmeyer

Statistics & Probability Letters, 1996, vol. 26, issue 1, 75-82

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.

Keywords: Functional; moments; Skewness; Decreasing; density (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (2)

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