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

TL;DR

This paper derives the distribution functions, expected values, and moments of linear combinations of lattice polynomials from the uniform distribution, which are important in various fields like optimization and game theory.

Contribution

It provides explicit formulas for distribution functions and moments of these polynomials, enhancing understanding of their probabilistic properties.

Findings

Derived distribution functions for linear combinations of lattice polynomials.

Calculated expected values and moments for these polynomials.

Applicable to aggregation theory, optimization, and game theory contexts.

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 Lovasz extensions.