Given a random set coming from the imprecise observation of a random variable, we study how to model the information about the distribution of this random variable. Specifically, we investigate whether the information given by the upper and lower probabilities induced by the random set is equivalent to the one given by the class of the distributions of the measurable selections; together with sufficient conditions for this, we also give examples showing that they are not equivalent in all cases.
Keywords. Random sets, upper and lower probabilities, measurable selections, Choquet integral
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Authors addresses:
Enrique Miranda
Department of Statistics and O. R.
C-Calvo Sotelo, s/n
33007 Oviedo (Spain)
In�s Couso
In�s Couso Blanco
Departamento de Estad�stica e I.O. y D.M.
Universidad de Oviedo
E.S. de Marina Civil
Carretera de Villaviciosa, s/n
33203 Gij�n, Spain
Pedro Gil
Department of Statistics and O. R.
C-Calvo Sotelo, s/n
33007 Oviedo (Spain)
E-mail addresses:
| Enrique Miranda | emiranda@correo.uniovi.es |
| In�s Couso | couso@pinon.ccu.uniovi.es |
| Pedro Gil | pedro@pinon.ccu.uniovi.es |