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Representing Uncertainty by Possibility Distributions Encoding Confidence Bands, Tolerance and Prediction Intervals

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Scalable Uncertainty Management (SUM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7520))

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Abstract

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.

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Author information

Authors and Affiliations

  1. IRIT, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Mohammad Ghasemi Hamed, Mathieu Serrurier & Nicolas Durand

  2. ENAC/MAIAA, 7 avenue Edouard Belin, 31055, Toulouse, France

    Mohammad Ghasemi Hamed & Nicolas Durand

Authors
  1. Mohammad Ghasemi Hamed
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  2. Mathieu Serrurier
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  3. Nicolas Durand
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Marburg University, Hans-Meerwein-Strasse 6, 35032, Marburg, Germany

    Eyke Hüllermeier , Thomas Fober  & Bernhard Seeger ,  & 

  2. Department of Computer Science, Auckland University, 38 Princes St., 1010, Auckland, New Zealand

    Sebastian Link

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Ghasemi Hamed, M., Serrurier, M., Durand, N. (2012). Representing Uncertainty by Possibility Distributions Encoding Confidence Bands, Tolerance and Prediction Intervals. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_18

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  • DOI: https://doi.org/10.1007/978-3-642-33362-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33361-3

  • Online ISBN: 978-3-642-33362-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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