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On Iterated Lorenz Curves With Applications

Author

Listed:
  • Zvetan Ignatov

    (Faculty of Economics and Business Administration, Sofia University St Kliment Ohridski)

  • Vilimir Yordanov

    (Technical University Vienna, Financial and Actuarial Mathematics)

Abstract

It is well known that a Lorenz curve, derived from the distribution function of a random variable, can itself be viewed as a probability distribution function of a new random variable (Arnold, 2015). We prove the surprising result that a sequence of consecutive iterations of this map leads to a non-corner case convergence, independent of the initial random variable. In the primal case, both the limiting distribution and its parent follow a power-law distribution with exponent equal to the golden section. In the reflected case, the limiting distribution is the Kumaraswamy distribution with a conjugate value of the exponent, while the parent distribution is the classical Pareto distribution. Potential applications are also discussed.

Suggested Citation

  • Zvetan Ignatov & Vilimir Yordanov, 2025. "On Iterated Lorenz Curves With Applications," Yearbook of the Faculty of Economics and Business Administration, Sofia University, Faculty of Economics and Business Administration, Sofia University St Kliment Ohridski - Bulgaria, vol. 24(1), pages 71-118, August.
    • Handle: RePEc:sko:yrbook:v:24:y:2025:i:1:p:71-118
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    References listed on IDEAS

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    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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