Pareto Distribution, Self-similarity and Empirics

  • Thomas Kämpke
  • Franz Josef Radermacher
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 679)


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”,


Poverty Line Gini Index Pareto Distribution Lorenz Curve Median Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thomas Kämpke
    • 1
  • Franz Josef Radermacher
    • 2
  1. 1.Research Institute for Applied Knowledge Processing (FAW/n)UlmGermany
  2. 2.Department of Computer ScienceUniversity of UlmUlmGermany

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