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Distribution functions of linear combinations of lattice polynomials from the uniform distribution

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  • Marichal, Jean-Luc
  • Kojadinovic, Ivan

Abstract

We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear combinations of order statistics, and lattice polynomials, are actually those continuous functions that reduce to linear functions on each simplex of the standard triangulation of the unit cube. They are mainly used in aggregation theory, combinatorial optimization, and game theory, where they are known as discrete Choquet integrals and Lovász extensions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:8:p:985-991
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    References listed on IDEAS

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    1. E. Algaba & J.M. Bilbao & J.R. Fernández & A. Jiménez, 2004. "The Lovász Extension of Market Games," Theory and Decision, Springer, vol. 56(1), pages 229-238, April.
    2. Michel Grabisch & Jean-Luc Marichal & Marc Roubens, 2000. "Equivalent Representations of Set Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 157-178, May.
    3. Marichal, Jean-Luc, 2006. "Cumulative distribution functions and moments of lattice polynomials," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1273-1279, July.
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