On the Proximity of a Probability to a Capacity Functional: Proximity Functions Articles uri icon

publication date

  • April 2008

start page

  • 264

end page

  • 287

issue

  • 2

volume

  • 24

international standard serial number (ISSN)

  • 1532-6349

electronic international standard serial number (EISSN)

  • 1532-4214

abstract

  • This paper aims to quantify the proximity of the distribution of a random vector in d to the distribution of a random set also in d. The latter is characterized by a capacity functional, so we introduce the notion of proximity function induced by a capacity functional as a mapping from the space of the probabilities on the Borel sigma-algebra on d, which assigns to each probability its degree of proximity to the capacity functional. Two particular proximity functions are considered and their properties are thoroughly analyzed, placing particular emphasis on their asymptotic behavior. An example where proximity functions are used to rank probabilities with respect to a capacity functional is discussed.