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Statistical Methods and Applications

, Volume 15, Issue 1, pp 75–88 | Cite as

Testing for Generalized Lorenz Dominance

  • Sangeeta AroraEmail author
  • Kanchan Jain
Original Article

Abstract

The Generalized Lorenz dominance can be used to take account of differences in mean income as well as income inequality in case of two income distributions possessing unequal means. Asymptotically distribution-free and consistent tests have been proposed for comparing two generalized Lorenz curves in the whole interval [p 1, p 2] where 0 < p 1 < p 2 < 1. Size and power of the test has been derived.

Keywords

Lorenz curve Generalized Asymptotic distribution Distribution free Power 

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References

  1. Atkinson AB (1970) On the measurement of Inequality. J Econ Theory 2:244–263CrossRefGoogle Scholar
  2. Beach CM, Davidson R (1983) Distribution-free statistical inference with Lorenz curves and income shares. Rev Econ Stud 50:723–735zbMATHCrossRefGoogle Scholar
  3. Billingsley P (1968) Convergence of probability measures. J Wiley, New YorkzbMATHGoogle Scholar
  4. Bishop JA, Chakraborti S, Thistle PD (1989) Asymptotically distribution-free statistical inference for generalized Lorenz curves. Rev Econ Stat LXXI:725–727CrossRefGoogle Scholar
  5. Chakraborti S (1994) Asymptotically distribution free joint confidence intervals for generalized Lorenz curves based on complete data. Stat Probab Lett 21:229–235zbMATHCrossRefGoogle Scholar
  6. Cszorgo M, Cszorgo S, Harvath L (1986) An asymptotic theory for Empirical Reliability and Concentration Processes. In: Brillinger et al (eds) Lecture notes in statistics, vol 33. Springer, Berlin Heidelberg New YorkGoogle Scholar
  7. Gastwirth JL (1971) A general definition of the Lorenz Curves. Econometrica 39:1037–1039zbMATHCrossRefGoogle Scholar
  8. Goldie CM (1977) Convergence theorems for empirical Lorenz curves and their inverses. Adv Appl Probab 9:765–791zbMATHCrossRefMathSciNetGoogle Scholar
  9. Hochberg Y, Tamhane AC (1987) Multiple comparison procedures. Wiley, New YorkzbMATHGoogle Scholar
  10. Kale BK, Singh H (1993) A test for Lorenz ordering between two distributions. In: Ghosh JK, Mitra SK, Parthasarathy KR, Prakash Rao BLS (eds) Statistics and probability: a Raghu Raj Bahadur Festschrift. Wiley Eastern Ltd., New Delhi, pp 293–302Google Scholar
  11. Lorenz MO (1905) Methods of measuring the concentration of wealth. Publ Am Stat Assoc 9:209–219CrossRefGoogle Scholar
  12. Rohtagi V (1988) An introduction to probability and mathematical statistics. Wiley Eastern Ltd., New DelhiGoogle Scholar
  13. Serfling RJ (1980) Approximation theorems of mathematical statistics. Wiley, New YorkzbMATHGoogle Scholar
  14. Shorrocks AF (1983) Ranking income distribution. Economica 50:3–17CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of StatisticsPanjab UniversityChandigarhIndia

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