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Cumulative distribution functions and moments of lattice polynomials

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  • Marichal, Jean-Luc

Abstract

We give the cumulative distribution functions, the expected values, and the moments of lattice polynomials when regarded as real functions. Since lattice polynomial functions include order statistics, our results encompass the corresponding formulas for order statistics.

Suggested Citation

  • Marichal, Jean-Luc, 2006. "Cumulative distribution functions and moments of lattice polynomials," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1273-1279, July.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:12:p:1273-1279
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    References listed on IDEAS

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    1. Ovchinnikov, Sergei, 1996. "Means on ordered sets," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 39-56, August.
    2. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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    Cited by:

    1. Marichal, Jean-Luc & Kojadinovic, Ivan, 2008. "Distribution functions of linear combinations of lattice polynomials from the uniform distribution," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 985-991, June.
    2. Michel Grabisch & Éric Raufaste, 2008. "An empirical study of statistical properties of Choquet and Sugeno integrals," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445168, HAL.
    3. Dukhovny, Alexander, 2007. "Lattice polynomials of random variables," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 989-994, June.

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