Reference : Multivariate integration of functions depending explicitly on the minimum and the max...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/2089
Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
1-May-2008
Journal of Mathematical Analysis & Applications
Elsevier
341
1
200-210
Yes (verified by ORBilu)
International
0022-247X
[en] multivariate integration ; Crofton formula ; aggregation function ; Cauchy mean ; distribution function ; expected value ; andness ; orness
[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.
University of Luxembourg - UL
Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/2089
10.1016/j.jmaa.2007.10.021
http://arxiv.org/abs/0710.2614

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