Choquet integral with stochastic entries

Abstract

We analyse the probabilistic features of the Choquet integral C µ (X) with respect to a capacity µ over {1, • • • , n}, where the n entries X = (X 1 , • • • , X n) are random variables. Few papers deal with this issue excepted in [8]. We give two different formula for the density function of C µ (X) when X 1 , • • • , X n are i.i.d. random variables. We also calculate the first moment of the Choquet integral and we compare our results with the ones obtained in [8] which mainly concern the cases where the common distribution of X i are either uniform or exponential.