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

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

2007-09-20

arxiv.org/abs/0709.3184v1

Statistics and Probability Letters 78 (8) (2008) 985-991

Mathematics

Probability

11 pages

Scientific paper

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 Lovasz extensions.

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