Weighted lattice polynomials of independent random variables
Jean-Luc Marichal
TL;DR
This paper derives formulas for the distribution, expectation, and moments of weighted lattice polynomials of independent random variables, extending to order statistics and applications in reliability analysis.
Contribution
It provides new formulas for weighted lattice polynomials, including order statistics, with an application to coherent system reliability analysis.
Findings
Derived cumulative distribution functions for weighted lattice polynomials.
Calculated expected values and moments for these polynomials.
Applied results to analyze reliability of coherent systems.
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.
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Taxonomy
TopicsData Management and Algorithms · Fuzzy Systems and Optimization · Probability and Risk Models