Representing uncertainty by possibility distributions encoding confidence bands, tolerance and prediction intervals

Mohammad Ghasemi Hamed (1) , Mathieu Serrurier (2) , Nicolas Durand (3, 4)

1 MAIA-OPTIM - ENAC Equipe MAIAA-OPTIM
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
3 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
4 IRIT-APO - Algorithmes Parallèles et Optimisation

For a given sample set, there are already different methods for building possibility distributions encoding the family of probability distributions that may have generated the sample set. Almost all the existing methods are based on parametric and distribution free confidence bands. In this work, we introduce some new possibility distributions which encode different kinds of uncertainties not treated before. Our possibility distributions encode statistical tolerance and prediction intervals (regions). We also propose a possibility distribution encoding the confidence band of the normal distribution which improves the existing one for all sample sizes. In this work we keep the idea of building possibility distributions based on intervals which are among the smallest intervals for small sample sizes. We also discuss the properties of the mentioned possibility distributions.

Mots clés: possibility distribution; imprecise probabilities; normal distribution; distribution free; tolerance interval; prediction interval; confidence band; confidence region

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Mohammad Ghasemi Hamed, Mathieu Serrurier, Nicolas Durand. Representing uncertainty by possibility distributions encoding confidence bands, tolerance and prediction intervals. SUM 2012, 6th International Conference on Scalable Uncertainty Management, Sep 2012, Marburg, Germany. pp 233-246, ⟨10.1007/978-3-642-33362-0_18⟩. ⟨hal-00938794⟩