Skip to main content
Springer Nature Link
Log in

Empirical Results Concerning a Fuzzy-Based Measure of Symmetry of Real Random Variables

  • Conference paper
Soft Methods for Handling Variability and Imprecision

Part of the book series: Advances in Soft Computing ((AINSC,volume 48))

  • 998 Accesses

Abstract

A new measure of skewness for real-valued random variables based on fuzzy tools has been recently introduced. The measure is derived from certain fuzzy representations of real-valued random variables which can be used to characterize the distribution of the original variables through the expected value of the ‘fuzzified’ random variables. In this communication, the empirical behaviour of an asymptotic testing procedure for the symmetry of real random variables based on this approach will be examined by simulating different distributions. Some advantages of the proposed test will be illustrated by means of these simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Mathware Soft. Comput. 2, 71–84 (1995)

    MATH  MathSciNet  Google Scholar 

  2. Cabaña, A., Cabaña, E.M.: Tests of symmetry based on transformed empirical processes. Canad. J. Statist. 28(4), 829–839 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Colubi, A., González-Rodríguez, G.: Triangular fuzzification of random variables and power of distribution tests: Empirical discussion. Comput. Statist. Data Anal. 51(9), 4742–4750 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Diamond, P., Kloeden, P.: Metric Spaces of Fuzzy Sets: Theory and Applications. World Scientific Publishing Co., Inc., River Edge (1994)

    MATH  Google Scholar 

  5. Dykstra, R., Kochar, S., Robertson, T.: Likelihood ratio tests for symmetry against one-sided alternatives. Annals of the Institute of Statistical Mathematics 47(4), 719–730 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gibbons, J.D., Chakraborti, S.: Nonparametric Statistical Inference, 4th edn. Statistics: Textbooks and Monographs, vol. 168. Marcel Dekker, Inc, New York (2003)

    MATH  Google Scholar 

  7. González-Rodríguez, G., Colubi, A., D’Urso, P., Giordani, P.: An asymptotic test about the asymmetry of random variables based on fuzzy tools. In: Lawry, J., Miranda, E., Bugarin, A., Li, S., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Integrated Uncertainty Modelling, pp. 87–94. Springer, Heidelberg (2006a)

    Google Scholar 

  8. González-Rodríguez, G., Colubi, A., Gil, M.A.: A fuzzy representation of random variables: an operational tool in exploratory analysis and hypothesis testing. Comput. Statist. Data Anal. 51(1), 163–176 (2006b)

    Article  MathSciNet  MATH  Google Scholar 

  9. González-Rodríguez, G., Colubi, A., Gil, M.A., D’Urso, P.: An asymptotic two dependent samples test of equality of means of fuzzy random variables. In: Proceedings of the 17th Conference of IASC-ERS (COMPSTAT 2006), pp. 689–695 (2006c)

    Google Scholar 

  10. González-Rodríguez, G., Montenegro, M., Colubi, A., Gil, M.A.: Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data. Fuzzy Sets Syst. 157(19), 2608–2613 (2006d)

    Article  MATH  Google Scholar 

  11. González-Rodríguez, G., Colubi, A., Gil, M.A., Lubiano, M.A.: A new way of quantifying the symmetry of a random variable: estimation and hypothesis testing (submitted for publication) (2008)

    Google Scholar 

  12. Hájek, J., Sidák, Z.: Theory of Rank Tests. Academic Press, New York (1967)

    MATH  Google Scholar 

  13. Klement, E.P., Puri, M.L., Ralescu, D.A.: Limit theorems for fuzzy random variables. Proc. R. Soc. Lond A. 407, 171–182 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  14. Körner, R., Näther, W.: On the variance of random fuzzy variables. In: Bertoluzza, C., Gil, M.A., Ralescu, D.A. (eds.) Statistical Modeling, Analysis and Management of Fuzzy Data. Studies in Fuzziness and Soft Computing, vol. 87, pp. 22–39. Physica-Verlag, Heildelberg (2002)

    Google Scholar 

  15. Mizushima, T., Nagao, H.: A test for symmetry based on density estimates. J. Japan Statist. Soc. 28(2), 205–225 (1998)

    MATH  MathSciNet  Google Scholar 

  16. Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning, Part 1. Inform. Sci. 8, 199–249; Part 2. Inform. Sci. 8, 301–353; Part 3. Inform. Sci. 9, 43–80 (1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Oviedo, Spain

    M. Asunción Lubiano & Ana Colubi

  2. European Centre for Soft Computing, Mieres, Spain

    Gil González-Rodríguez

Authors
  1. M. Asunción Lubiano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ana Colubi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gil González-Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Université Paul Sabatier, Toulouse, France

    Didier Dubois  & Henri Prade  & 

  2. Universidad de Oviedo, Spain

    M. Asunción Lubiano  & María Ángeles Gil  & 

  3. Polish Academy of Sciences, Warsaw, Poland

    Przemysław Grzegorzewski

  4. Polish Academy of Sciences,, Warsaw, Poland

    Olgierd Hryniewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lubiano, M.A., Colubi, A., González-Rodríguez, G. (2008). Empirical Results Concerning a Fuzzy-Based Measure of Symmetry of Real Random Variables. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85027-4_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85026-7

  • Online ISBN: 978-3-540-85027-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics