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Interval-valued quantification of the inequality associated with a random set

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  • López-García, Hortensia
  • López-Díaz, Miguel
  • Gil, María Angeles

Abstract

In this paper we formalize the measurement of the inequality associated with a (compact convex) random set, by considering this last notion to model interval-valued random variables whose values are allowed to overlap, and extending the well-known family of the Gastwirth inequality indices. We analyze the fundamental properties of the extended indices and illustrate their use.

Suggested Citation

  • López-García, Hortensia & López-Díaz, Miguel & Gil, María Angeles, 2000. "Interval-valued quantification of the inequality associated with a random set," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 149-159, January.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:2:p:149-159
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    References listed on IDEAS

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    1. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    2. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    3. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    4. Frank A. Cowell & Fatemeh Mehta, 1982. "The Estimation and Interpolation of Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 273-290.
    5. Gastwirth, Joseph L & Nayak, Tapan K & Krieger, Abba 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, American Statistical Association, vol. 4(2), pages 269-273, April.
    6. Cowell, Frank A., 1991. "Grouping bounds for inequality measures under alternative informational assumptions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 1-14.
    7. Gil, María Angeles & Gil, Pedro, 1989. "On some information measures of degree [beta] = 2: estimation in simple-stage cluster sampling," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 157-162, June.
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