Lorenz Curves and Generalised Entropy Inequality Measures

  • Nicholas Rohde
Part of the Economic Studies in Equality, Social Exclusion and Well-Being book series (EIAP, volume 5)


Lorenz curves and Generalised Entropy (GE) measures are popular tools for analyzing income inequality. This paper seeks to connect these techniques by demonstrating that GE inequality measures may be derived directly from the Lorenz curve. The paper provides analytical expressions for Theil’s T and L inequality measures, half the square of the coefficient of variation and Atkinson’s utility based measure in terms of the Lorenz curve. Mathematical expressions for common GE measures are derived for three simple parametric specifications. The results are empirically illustrated and shown to be consistent with Lorenz dominance.


Income Inequality Generalise Entropy Lorenz Curve Inequality Measure Income Share 


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  1. Atkinson, A. B. (1970) On the Measurement of Inequality, Journal of Economic Theory, 2, 244-263. CrossRefGoogle Scholar
  2. Chotikapanich, D. (1993) A Comparison of Alternative Functional Forms for the Lorenz Curve, Economics Letters, 41, 129-138.CrossRefGoogle Scholar
  3. Cowell, F. (1995) Measuring Inequality, 2nd ed., Harvester Wheatsheaf. Hemel Hempstead.Google Scholar
  4. Dowrick, S. and M. Akmal (2005) Contradictory Trends in Global Income Inequality: A Tale of Two Biases, Review of Income and Wealth, 51, 201-229.CrossRefGoogle Scholar
  5. Gupta, M. (1984) Functional Form for Estimating the Lorenz Curve: Note, Econometrica, 52, 1313-1314.CrossRefGoogle Scholar
  6. Hildebrand, F. (1962) Advanced Calculus for Applications, Prentice Hall, New Jersey.Google Scholar
  7. Kakwani, N. (1980) Income Inequality and Poverty: Methods of Estimation and Policy Applications, Oxford University Press, Oxford.Google Scholar
  8. Kakwani, N. and N. Podder (1973) On the Estimation of Lorenz Curves from Grouped Observations, International Economic Review, 14, 278-292.CrossRefGoogle Scholar
  9. Milanovic, B. (2002) True World Income Distribution, 1988 and 1993: First Calcu-lation Based on Household Surveys Alone, Economic Journal, 112, 51-92.CrossRefGoogle Scholar
  10. Sala-i Martin, X. (2002) The World Distribution of Income (Estimated from Indi-vidual Country Distributions), NBER Working Paper 8905, pp. 1-68.Google Scholar
  11. Schutz, R. R. (1951) On the Measurement of Income Inequality, American Eco-nomic Review, 41, 107-122.Google Scholar
  12. Theil, H. (1979) World Income Inequality and its Components, Economics Letters, 2, 99-102.CrossRefGoogle Scholar
  13. Theil, H. (1967) Economics and Information Theory, North Holland, Amsterdam.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Nicholas Rohde
    • 1
  1. 1.School of EconomicsThe University of QueenslandBrisbaneAustralia

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