Pareto Distribution, Self-similarity and Empirics

Thomas Kämpke and Franz Josef Radermacher
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Thomas Kämpke: Research Institute for Applied Knowledge Processing (FAW/n)
Franz Josef Radermacher: University of Ulm

Chapter Chapter 7 in Income Modeling and Balancing, 2015, pp 103-128 from Springer

Abstract: Abstract A one-parametric version of the Pareto distribution can be obtained as unique solution of a differential equation for Lorenz curves. This distribution, also, is unique among self-similar Lorenz curves as well as among all so-called Gini self-similar Lorenz curves. Median self-similarity leads to a wider solution manifold but every function of this manifold is interpolated by a Pareto distribution. The Pareto distribution is also obtainable from an iterative process that considers every Lorenz curve as a distribution function. Parameters of best fit Pareto distributions are given for empirical income data. These show a great imbalance for the world as a whole and indicate that the most prosperous nations lie in a “productive inequality range”. Some remarks to changes in social balance over the last decade are given. Also, there is a reference to Thomas Piketty’s important work “Capital in the 21st century”,

Keywords: Poverty Line; Gini Index; Pareto Distribution; Lorenz Curve; Median Parameter (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-319-13224-2_7

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DOI: 10.1007/978-3-319-13224-2_7

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