ON ITERATED LORENZ CURVES WITH APPLICATIONS

Zvetan Ignatov and Vilimir Yordanov ()
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Zvetan Ignatov: Faculty of Economics and Business Administration, Sofia University St Kliment Ohridski
Vilimir Yordanov: Technical University Vienna, Financial and Actuarial Mathematics

Yearbook of the Faculty of Economics and Business Administration, Sofia University, 2025, vol. 24, issue 1, 71-118

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.

Keywords: Lorenz curve; iteration; contraction mapping; golden section; Mathematics Subject Classification - 39B12; 60F99; 62G30; 62G32; 62P05 (search for similar items in EconPapers)
JEL-codes: C02 (search for similar items in EconPapers)
Date: 2025
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