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Strassen's LIL for the Lorenz Curve

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  • Csörgo, Miklós
  • Zitikis, Ricardas
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    Abstract

    We prove Strassen's law of the iterated logarithm for the Lorenz process assuming that the underlying distribution functionFand its inverseF-1are continuous, and the momentEX2+[var epsilon]is finite for some[var epsilon]>0. Previous work in this area is based on assuming the existence of the densityf:=F' combined with further assumptions onFandf. Being based only on continuity and moment assumptions, our method of proof is different from that used previously by others, and is mainly based on a limit theorem for the (general) integrated empirical difference process. The obtained result covers all those we are aware of on the LIL problem in this area.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 59 (1996)
    Issue (Month): 1 (October)
    Pages: 1-12

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    Handle: RePEc:eee:jmvana:v:59:y:1996:i:1:p:1-12

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    Related research

    Keywords: Lorenz curve Lorenz process Strassen's law of the iterated logarithm Vervaat process integrated empirical difference process empirical process quantile process relative compactness mean residual life process total time on test function Lorenz process of order[nu] Shannon process redudancy process;

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    Cited by:
    1. 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.
    2. 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.
    3. 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.
    4. 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.

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