Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables

Details Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables

2007-10-13

arxiv.org/abs/0710.2614v1

Journal of Mathematical Analysis and Applications 341 (1) (2008) 200-210

Mathematics

Functional Analysis

15 pages

Scientific paper

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.

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