On the Variation of the f-Inequality of a Random Variable

  • I. Cascos-Fernández
  • M. López-Díaz
  • M. A. Gil-Álvarez
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 16)


In this paper we recall the definition of a generalized inequality index of a real-valued random variable, and present some new useful properties in which we analyze how this index varies in terms of the variable variation. This will serve us in a future to state set-valued inequality indices for certain random sets.


Convex Function Variable Variation Inequality Index Fuzzy Random Variable Positive Random Variable 


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  1. 1.
    Alonso, M.C., Brezmes, T., Lubiano, M.A. and Bertoluzza C. (2001) A generalized real-valued measure of the inequality associated with a fuzzy random variable. Int. J. Approx. Reason. 26, 47–66.Google Scholar
  2. 2.
    Bourguignon, F. (1979) Decomposable income inequality measures. Econometrica 47, 901–920.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Cascos, I. (2001) Asymptotic Results on Inequality Indices for Radom Sets. Master Thesis. Universidad de Oviedo.Google Scholar
  4. 4.
    Colubi, A. (1997) The fuzzy f-inequality indices associated to a fuzzy random variable (in Spanish). Master Thesis. Universidad de Oviedo.Google Scholar
  5. 5.
    Csiszâr, I. (1967) Information-type mesaures of difference of probability distributions and indirect observations. Studia Scient. Math. Hung. 2, 299–318.Google Scholar
  6. 6.
    Gastwirth, J.L. (1975) The Estimation of a Family of Measures of Economic Inequality. Journal of Econometrics 3, 61–70.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Gastwirth, J.L., Nayak, T.K. and Krieger, A.M. (1986) Large Sample Theory for the Bounds on the Gini and Related Indices of Inequality Estimated From Grouped Data. Journal of Business & Economic Statistics 4, 269–273.Google Scholar
  8. 8.
    Lubiano Gómez, M.A. (1998) Variation measures for imprecise random elements. PhD Thesis. Universidad de Oviedo.Google Scholar
  9. 9.
    Shaked, M. and Shanthikumar, J.G. (1994) Stochastic Orders and Their Applications. Academic Press. Boston.MATHGoogle Scholar
  10. 10.
    Rockafellar, R.T. (1970) Convex Analysis. Princeton University Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • I. Cascos-Fernández
    • 1
  • M. López-Díaz
    • 1
  • M. A. Gil-Álvarez
    • 1
  1. 1.Dpto. de Estadística e I.O. y D.M.Universidad de OviedoOviedoSpain

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