On the moments and distribution of discrete Choquet integrals from continuous distributions

TL;DR

This paper investigates the moments and distribution of discrete Choquet integrals for samples from continuous distributions, providing new insights into their behavior and applications in aggregation functions.

Contribution

It extends existing results from the uniform case to other distributions like exponential and normal, and explores asymptotic properties of the Choquet integral.

Findings

Derived moments for exponential distribution

Provided approximation methods for normal distribution

Analyzed asymptotic distribution of the Choquet integral

Abstract

We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means, ordered weighted averaging functions, and lattice polynomial functions as particular cases, our results encompass the corresponding results for these aggregation functions. After detailing the results obtained in [1] in the uniform case, we present results for the standard exponential case, show how approximations of the moments can be obtained for other continuous distributions such as the standard normal, and elaborate on the asymptotic distribution of the Choquet integral. The results presented in this work can be used to improve the interpretation of discrete Choquet integrals when employed as aggregation functions.