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Pareto Distribution, Self-similarity and Empirics

In: Income Modeling and Balancing

Author

Listed:
  • Thomas Kämpke

    (Research Institute for Applied Knowledge Processing (FAW/n))

  • Franz Josef Radermacher

    (University of Ulm)

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”,

Suggested Citation

  • Thomas Kämpke & Franz Josef Radermacher, 2015. "Pareto Distribution, Self-similarity and Empirics," Lecture Notes in Economics and Mathematical Systems, in: Income Modeling and Balancing, edition 127, chapter 0, pages 103-128, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-13224-2_7
    DOI: 10.1007/978-3-319-13224-2_7
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