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Soft Methods for Integrated Uncertainty Modelling pp 87–94Cite as

An Asymptotic Test for Symmetry of Random Variables Based on Fuzzy Tools

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Part of the book series: Advances in Soft Computing ((AINSC,volume 37))

Abstract

A new measure of skewness for real random variables is proposed in this paper. The measure is based on a fuzzy representation of real-valued random variables which can be used to characterize the distribution of the original variable through the expected value of the ‘fuzzified’ random variable. Inferential studies concerning the expected value of fuzzy random variables provide us with a tool to analyze the asymmetry degree from random samples. As a first step, we propose an asymptotic test of symmetry. We present some examples and simulations to illustrate the behaviour of the proposed test.

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Author information

Authors and Affiliations

  1. Dpto. de Estadística e I.O., Universidad de Oviedo, 33007, Spain

    González-Rodríguez G. & Colubi A.

  2. Dpto. di Scienze Economiche, Gestionali e Sociali. UniversitZà degli Studi del Molise, 86100, Italy

    D’Urso P.

  3. Dpto. di Statistica, Probabilità e Statistiche Applicate, Università degli Studi di Roma “La Sapienza”, 00185, Italy

    Giordani P.

Authors
  1. González-Rodríguez G.
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  2. Colubi A.
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  3. D’Urso P.
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  4. Giordani P.
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Editor information

Editors and Affiliations

  1. AI Group Department of Engineering Mathematics, University of Bristol, BS8 1TR, Bristol, UK

    Jonathan Lawry

  2. Statistics and Operations Research, Rey Juan Carlos University, C-Tulip˙n s/n MÛstoles28933, Spain

    Enrique Miranda

  3. Intelligent Systems Group Department of Electronics & Computer Science, University of Santiago de Compostela Santiago de Compostela, Spain

    Alberto Bugarin

  4. Department of Applied Mathematics, Beijing University of Technology, 100022, Beijing, P.R. China

    Shoumei Li

  5. Dpto. Estadistica e I.O y D.M. Calle Calvo Sotelo s/n, Universiad de Oviedo Fac. Ciencias, 33071, Oviedo, Spain

    Maria Angeles Gil

  6. Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemys aw Grzegorzewski

  7. Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Olgierd Hyrniewicz

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© 2006 Springer

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G., GR., A., C., P., D., P., G. (2006). An Asymptotic Test for Symmetry of Random Variables Based on Fuzzy Tools. In: Lawry, J., et al. Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-34777-1_12

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  • DOI: https://doi.org/10.1007/3-540-34777-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34776-7

  • Online ISBN: 978-3-540-34777-4

  • eBook Packages: EngineeringEngineering (R0)

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