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.Comment: 11 page
