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On the connection between probability boxes and possibility measures

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


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
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