Reference : On the moments and distribution of discrete Choquet integrals from continuous distrib...
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On the moments and distribution of discrete Choquet integrals from continuous distributions
Kojadinovic, Ivan mailto [The University of Auckland, Auckland, New Zealand > Department of Statistics]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Journal of Computational and Applied Mathematics
Elsevier Science
Yes (verified by ORBilu)
The Netherlands
[en] discrete Choquet integral ; Lovász extension ; order statistic ; B-Spline ; divided difference ; asymptotic distribution
[en] 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.
University of Luxembourg - UL
F1R-CSC-PUL-08RMSD > RMSD > 01/04/2008 – 31/12/2011 > BISDORFF Raymond
Researchers ; Professionals ; Students

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