We investigate the properties of the upper probability associated with a bivariate p-box, that may be used as a model for the imprecise knowledge of a bivariate distribution function. We give necessary and sufficient conditions for this upper probability to be maxitive, characterize its focal elements, and study which maxitive functions can be obtained as upper probabilities of bivariate p-boxes.


Coherent lower and upper probabilities Uni- and bivariate p-boxes Maxitive functions Focal sets Random sets 



The research reported in this paper has been supported by project TIN2014-59543-P.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of StatisticsCarlos III University of MadridGetafeSpain
  2. 2.Department of Statistics and Operations ResearchUniversity of OviedoOviedoSpain

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