On Iterated Lorenz Curves with Applications (2401.13183v3)

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 [4]. 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 coefficient equal to the golden ratio. In the reflected case, the limiting distribution is the Kumaraswamy distribution with a conjugate coefficient, while the parent distribution is the classical Pareto distribution. Potential applications are also discussed.