lattice polynomial
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2019 ◽  
Vol 368 ◽  
pp. 101-118
Author(s):  
Quentin Brabant ◽  
Miguel Couceiro ◽  
José Rui Figueira

2012 ◽  
Vol 28 (1) ◽  
pp. 167-184 ◽  
Author(s):  
Alexander Dukhovny ◽  
Jean-Luc Marichal
Keyword(s):  

2010 ◽  
Vol 81 (3) ◽  
pp. 263-278 ◽  
Author(s):  
Miguel Couceiro ◽  
Erkko Lehtonen

2008 ◽  
Vol 22 (3) ◽  
pp. 373-388 ◽  
Author(s):  
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 its components. As such, the concept of a random variable Y defined by a weighted lattice polynomial of (lattice-valued) random variables is considered in general and in some special cases. The central object of interest is the cumulative distribution function of Y. In particular, numerous results are obtained for lattice polynomials and weighted lattice polynomials in the case of independent arguments and in general. For the general case, the technique consists in considering the joint probability generating function of “indicator” variables. A connection is studied between Y and order statistics of the set of arguments.


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