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Odd central moments of unimodal distributions

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  • Bélisle, Claude

Abstract

We present a simple geometric condition under which all existing odd central moments of a unimodal distribution are non-negative. The criterion applies to both the absolutely continuous case and the lattice case. In the lattice case, the result proves and generalizes a conjecture of Frame, Gilliland and Hsing. In the absolutely continuous case, the result provides a new proof of results of Hannan and Pitman, Runnenburg, and MacGillivray. The main idea is a new decomposition result for unimodal distributions.

Suggested Citation

  • Bélisle, Claude, 1991. "Odd central moments of unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 97-107, August.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:2:p:97-107
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    Cited by:

    1. Averous, J. & Fougères, A. -L. & Meste, M., 1996. "Tailweight with respect to the mode for unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 367-373, August.
    2. 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.

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