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Applications of the Gini Index Beyond Economics and Statistics

In: Handbook of the Mathematics of the Arts and Sciences

Author

Listed:
  • Roberta La Haye

    (Mount Royal University)

  • Petr Zizler

    (Mount Royal University)

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.

Suggested Citation

  • Roberta La Haye & Petr Zizler, 2021. "Applications of the Gini Index Beyond Economics and Statistics," Springer Books, in: Bharath Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, chapter 65, pages 1661-1689, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-57072-3_103
    DOI: 10.1007/978-3-319-57072-3_103
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