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The β Family of Inequality Measures


  • Luis José Imedio Olmedo

    () (Dpto. Estadistica y Econometria (68). Facultad de Ciencias Economicas y Empresariales. Campus El Ejido s/n. Universidad de Malaga, 29013 Malaga.)

  • Encarnación M. Parrado Gallardo

    () (Dpto. Estadistica y Econometria (68). Facultad de Ciencias Economicas y Empresariales. Campus El Ejido s/n. Universidad de Malaga, 29013 Malaga)

  • Elena Bárcena Martín

    () (Dpto. Estadistica y Econometria (68). Facultad de Ciencias Economicas y Empresariales. Campus El Ejido s/n. Universidad de Malaga, 29013 Malaga. Telf. +34 952 131 191)


This paper introduces and analyses, both normatively and statistically, a new class of inequality measures. This class generalizes and comprises different well-known families of inequality measures as particular cases. The elements of this new class are obtained by weighting local inequality evaluated through the Bonferroni curve. The weights are the density functions of the beta distributions over [0,1]. Therefore, the weights are not necessarily monotonic. This allows us to choose the inequality measures that are more or less sensitive to changes that could take place in any part of the distribution. As a consequence of the different weighting schemes attached to the indexes, the elements of the class introduce very dissimilar value judgements in the measurement of inequality and welfare. The possibility of choosing the index that focuses on a specific percentile, and not necessarily on the extremes of the distribution, is one of the advantages of our proposal.

Suggested Citation

  • Luis José Imedio Olmedo & Encarnación M. Parrado Gallardo & Elena Bárcena Martín, 2013. "The β Family of Inequality Measures," Working Papers 289, ECINEQ, Society for the Study of Economic Inequality.
  • Handle: RePEc:inq:inqwps:ecineq2013-289

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    References listed on IDEAS

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    More about this item


    Lorenz curve; Bonferroni curve; preference distributions; inequality aversion; beta distribution;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

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