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Handbook of the Mathematics of the Arts and Sciences pp 1–29Cite as

Applications of the Gini Index Beyond Economics and Statistics

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Abstract

This chapter discusses the Gini index and Gini mean difference, two closely related statistics that have vastly different applications. These applications include traditional ones such as income and wealth as well as nontraditional ones arising in such diverse fields such as digital imaging, genetics, and astronomy. The Gini index and Gini mean difference are defined in terms of the Lorenz curve. The Lorenz curve allows the development of a geometric intuition regarding the quantities involved. The curve provides an interesting perspective on how the Gini index and the Gini mean difference change under various scenarios involving household income inequality in a country. The Lorenz curve and Gini’s two measures are further explored in the context of measuring contrast in grayscale images as well. The coefficient of variation and standard deviation are also discussed for the sake of comparison, and several other measures of spread and inequality arising in the Lorenz curve are noted.

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References

  • Abraham R, van der Bergh S, Nair P (2003) A new approach to Galaxy morphology: I. Analysis of the sloan digital sky survey early data release. Astrophys J 588:218–229. https://doi.org/10.1086/373919

    Article  Google Scholar 

  • Catalano M, Leise T, Pfaff T (2009) Measuring resource inequality: the Gini coefficient. Numeracy 2:1–22

    Article  Google Scholar 

  • Dalton H (1920) Measurement of the Inequality of Income. Econ J 30:348–361

    Article  Google Scholar 

  • Farris F (2010) The Gini index and measures of inequality. Am Math Mon 117:851–864

    Article  MathSciNet  Google Scholar 

  • Gastwirth J (1971) A general definition of the Lorenz curve. Econometrica 39:1037–1039

    Article  Google Scholar 

  • Gastwirth J (1972) The estimation of the Lorenz curve and Gini index. Rev Econ Stat 54:306–316

    Article  MathSciNet  Google Scholar 

  • Gerstenberger C, Vogel D (2015) On the efficiency of Gini’s mean difference. Stat Methods Appl 24:569–596

    Article  MathSciNet  Google Scholar 

  • Giorgi G, Gubbiotti S (2017) Celebrating the memory of corrado Gini: a personality out of the ordinary. Int Stat Rev 85:325–339

    Article  MathSciNet  Google Scholar 

  • Hurley N, Ricard S (2009) Comparing measures of sparsity. IEEE Trans Inform Theory 55:4723–4741

    Article  MathSciNet  Google Scholar 

  • Jantzen R, Volpert K (2012) On the mathematics of income inequality: splitting the Gini index in two. Am Math Mon 119:824–837

    Article  MathSciNet  Google Scholar 

  • Kendall M, Stuart A, Ord J (1987) Kendall’s advanced theory of statistics, vol 1, 5th edn. Oxford University Press, New York

    MATH  Google Scholar 

  • La Haye R, Zizler P (2018) The Gini index and grayscale images. Coll Math J 49:205–211

    Article  MathSciNet  Google Scholar 

  • La Haye R, Zizler P (2019) The Gini mean difference and variance. Metron 77:43–52

    Article  MathSciNet  Google Scholar 

  • O’Hagan S, Muelas M, Day P, D K (2018) GeneGini: assessment via the Gini coefficient of reference “housekeeping” genes and diverse human transporter expression profile. Cell Syst 6:230–244. https://doi.org/10.1016/j.cels.2018.01.003

  • Piesch W (2005) A look at the structure of some extended Ginis. Int J Stat 63:263–296

    MathSciNet  MATH  Google Scholar 

  • Saha D, Kemanian A, Montes F, Gall H, Adler P, Rau B (2018) Lorenz curve and Gini coefficient reveal hot spots and hot moments for nitrous oxide emissions. J Geophys Res-Biogeo 123: 193–206

    Article  Google Scholar 

  • Wang X, Zhang J, Shahid S, AlMahdi E, He R, Wang X, Ali M (2012) Gini coefficient to assess equity in domestic water supply in the Yellow River. Mitig Adapt Strateg Glob Change 17: 65–75

    Article  Google Scholar 

  • Yitzhaki S (1997) More than a dozen alternative ways of spelling Gini. Res Econ Inequality 8: 13–30

    Google Scholar 

  • Yitzhaki S (2003) Gini’s mean difference: a superior measure of variability for non-normal distributions. Metron 61:285–316

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Mount Royal University, Calgary, AB, Canada

    Roberta La Haye & Petr Zizler

Authors
  1. Roberta La Haye
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  2. Petr Zizler
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Correspondence to Petr Zizler .

Editor information

Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

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Haye, R., Zizler, P. (2020). Applications of the Gini Index Beyond Economics and Statistics. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_103-1

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  • DOI: https://doi.org/10.1007/978-3-319-70658-0_103-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70658-0

  • Online ISBN: 978-3-319-70658-0

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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