Summary
The asymptotic distribution for a certain class of functionals of distribution functions is derived. This result is used to give distribution free asymptotic confidence intervals for these functionals; for this purpose, a strongly consistent estimate for the asymptotic variance is constructed. These results are applied to the Lorenz-curve and the Gini-measure as special cases of the abovementioned class of functionals.
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Sendler, W. On statistical inference in concentration measurement. Metrika 26, 109–122 (1979). https://doi.org/10.1007/BF01893478
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DOI: https://doi.org/10.1007/BF01893478