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On the rate of strong consistency of Lorenz curves

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  • Csörgö, Miklós
  • Zitikis, Ricardas

Abstract

Assuming the finiteness of only the second moment, we prove that LIL for Lorenz curves holds true provided that the underlying distribution function and its inverse are continuous. The proof is crucially based on a limit theorem for the general Vervaat process.

Suggested Citation

  • Csörgö, Miklós & Zitikis, Ricardas, 1997. "On the rate of strong consistency of Lorenz curves," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 113-121, June.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:2:p:113-121
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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. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    3. Csörgo, Miklós & Zitikis, Ricardas, 1996. "Strassen's LIL for the Lorenz Curve," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 1-12, October.
    4. Rao, C. R., 1995. "Strassen's Law of the Iterated Logarithm for the Lorenz Curves," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 239-252, August.
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    Cited by:

    1. Sze-Man Tse, 2006. "Lorenz Curve for Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 675-686, December.
    2. Csörgo, Miklós & Zitikis, Ricardas, 1998. "On the Rate of Strong Consistency of the Total Time on Test Statistic," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 99-117, July.
    3. Bongiorno, Enea G. & Goia, Aldo, 2019. "Describing the concentration of income populations by functional principal component analysis on Lorenz curves," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 10-24.
    4. Tse, SzeMan, 2011. "Composing the cumulative quantile regression function and the Goldie concentration curve," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 674-682, March.
    5. Fakoor, V. & Ghalibaf, M. Bolbolian & Azarnoosh, H.A., 2011. "Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1425-1435, September.

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