Article (Scientific journals)
On the moments and distribution of discrete Choquet integrals from continuous distributions
Kojadinovic, Ivan; Marichal, Jean-Luc
2009In Journal of Computational and Applied Mathematics, 230 (1), p. 83-94
Peer reviewed
 

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Keywords :
discrete Choquet integral; Lovász extension; order statistic; B-Spline; divided difference; asymptotic distribution
Abstract :
[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.
Disciplines :
Mathematics
Quantitative methods in economics & management
Identifiers :
UNILU:UL-ARTICLE-2010-414
Author, co-author :
Kojadinovic, Ivan;  The University of Auckland, Auckland, New Zealand > Department of Statistics
Marichal, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
On the moments and distribution of discrete Choquet integrals from continuous distributions
Publication date :
01 August 2009
Journal title :
Journal of Computational and Applied Mathematics
ISSN :
0377-0427
Publisher :
Elsevier Science, Amsterdam, Netherlands
Volume :
230
Issue :
1
Pages :
83-94
Peer reviewed :
Peer reviewed
Name of the research project :
F1R-CSC-PUL-08RMSD > RMSD > 01/04/2008 – 31/12/2011 > BISDORFF Raymond
Funders :
University of Luxembourg - UL
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since 24 June 2013

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