55 citations · 565 across the 70 of their papers we have counts for
9 papers · 1 filter
System reliability and weighted lattice polynomials
Alexander Dukhovny, Jean-Luc Marichal
The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of…
Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables
Jean-Luc Marichal
By using some basic calculus of multiple integration, we provide an alternative expression of the integral in whic…
Distribution functions of linear combinations of lattice polynomials from the uniform distribution
Jean-Luc Marichal, Ivan Kojadinovic
We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice…
On perfect, amicable, and sociable chains
Jean-Luc Marichal
Let be an n-chain, i.e., an n-tuple of non-negative integers . Consider the operator , where x'_j represents the…
Weighted lattice polynomials of independent random variables
Jean-Luc Marichal
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.…
Approximations of Lovasz extensions and their induced interaction index
Jean-Luc Marichal, Pierre Mathonet
The Lovasz extension of a pseudo-Boolean function is defined on each simplex of the standard triangulation of as the unique affine function $\hat f…