Article (Scientific journals)
Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables
Marichal, Jean-Luc
2008In Journal of Mathematical Analysis and Applications, 341 (1), p. 200-210
Peer reviewed
 

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Keywords :
multivariate integration; Crofton formula; aggregation function; Cauchy mean; distribution function; expected value; andness; orness
Abstract :
[en] By using some basic calculus of multiple integration, we provide an alternative expression of the integral $$ \int_{]a,b[^n} f(\mathbf{x},\min x_i,\max x_i) \, d\mathbf{x}, $$ in which the minimum and the maximum are replaced with two single variables. We demonstrate the usefulness of that expression in the computation of orness and andness average values of certain aggregation functions. By generalizing our result to Riemann-Stieltjes integrals, we also provide a method for the calculation of certain expected values and distribution functions.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-ARTICLE-2010-410
Author, co-author :
Marichal, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables
Publication date :
01 May 2008
Journal title :
Journal of Mathematical Analysis and Applications
ISSN :
0022-247X
Publisher :
Elsevier
Volume :
341
Issue :
1
Pages :
200-210
Peer reviewed :
Peer reviewed
Name of the research project :
Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond
Funders :
University of Luxembourg - UL
Available on ORBilu :
since 23 May 2013

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