Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

On statistical inference in concentration measurement

  • 44 Accesses

  • 21 Citations


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.

This is a preview of subscription content, log in to check access.


  1. Billingsley, P.: Convergence of Probability measures, 1968.

  2. Bruckmann, G.: Einige Bemerkungen zur statistischen Messung der Konzentration. Metrika14, 1969, 183–213.

  3. Loéve, M.: Probability Theory. 3. ed., 1963

  4. Piesch, W.: Statistische Konzentrationsmaße. Tübinger Wissenschaftliche Abhandlungen, 1975.

  5. Shorack, G.: Functions of order statistics. Ann. Math. Stat.43, 1972, 412–427.

  6. Wellner, J.A.: A Glivenko-Cantelli Theorem and Strong Laws of Large Numbers for Functions of Order Statistics. Ann. Stat.5, 1977, 473–480.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sendler, W. On statistical inference in concentration measurement. Metrika 26, 109–122 (1979). https://doi.org/10.1007/BF01893478

Download citation


  • Confidence Interval
  • Distribution Function
  • Stochastic Process
  • Probability Theory
  • Economic Theory