  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.
