Abstract
The law of large numbers for coherent lower previsions (specifically, Choquet integrals against belief measures) can be applied to possibility measures, yielding that sample averages are asymptotically confined in a compact interval. This interval differs from the one appearing in the law of large numbers from possibility theory. In order to understand this phenomenon, we undertake an in-depth study of the compatibility of the assumptions in those results. It turns out that, although there is no incompatibility between their conclusions, their assumptions can only be simultaneously satisfied if the possibility distributions of the variables are 0–1 valued.
The first author’s research in this paper was partially funded by Asturias’s Consejería de Economía y Empleo (FC-15-GRUPIN14-101) and by Spain’s Ministerio de Economía y Competitividad (MTM2015–63971–P).
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Terán, P., Pis Vigil, E. (2018). Contrasting Two Laws of Large Numbers from Possibility Theory and Imprecise Probability. In: Destercke, S., Denoeux, T., Cuzzolin, F., Martin, A. (eds) Belief Functions: Theory and Applications. BELIEF 2018. Lecture Notes in Computer Science(), vol 11069. Springer, Cham. https://doi.org/10.1007/978-3-319-99383-6_30
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DOI: https://doi.org/10.1007/978-3-319-99383-6_30
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