Weighted lattice polynomials of independent random variables

Authors:
Jean-Luc Marichal
Affiliations:
Applied Mathematics Unit, University of Luxembourg, 162A, avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include ordinary lattice polynomial functions and, particularly, order statistics, our results encompass the corresponding formulas for these particular functions. We also provide an application to the reliability analysis of coherent systems.