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On the connection between probability boxes and possibility measures

By Matthias C. M. Troffaes, Enrique Miranda and Sebastien Destercke

Abstract

We explore the relationship between possibility measures (supremum preserving normed measures) and p-boxes (pairs of cumulative distribution functions) on totally preordered spaces, extending earlier work in this direction by De Cooman and Aeyels, among others. We start by demonstrating that only those p-boxes who have 0-1-valued lower or upper cumulative distribution function can be possibility measures, and we derive expressions for their natural extension in this case. Next, we establish necessary and sufficient conditions for a p-box to be a possibility measure. Finally, we show that almost every possibility measure can be modelled by a p-box. Whence, any techniques for p-boxes can be readily applied to possibility measures. We demonstrate this by deriving joint possibility measures from marginals, under varying assumptions of independence, using a technique known for p-boxes. Doing so, we arrive at a new rule of combination for possibility measures, for the independent case.Comment: 24 pages, 3 figure

Topics: Mathematics - Probability, Mathematics - Statistics Theory, 28B02, 60E99, 62E86, G.3
Year: 2011
DOI identifier: 10.1016/j.ins.2012.09.033
OAI identifier: oai:arXiv.org:1103.5594
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