Transfer and Distribution Approximation

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


Pigou–Dalton transfers carry over to complex income distributions under convergence in distribution and, thus, make these complex distributions comparable. While finite sequences of Pigou–Dalton transfers amount to majorization, convergence results extend these to the convex stochastic order for distributions with equal means. Thus, the larger of any two such distributions can be decreased to the smaller by Pigou–Dalton transfers and a limiting process. Alternatively, the same result can be obtained by probabilistic, more comprehensive Pigou–Dalton transfers, allowing a simpler approximation.

Also, absolute and progressive taxation are shown to decrease in the Lorenz order any Lorenz curve of a finite income distribution.


Taxation Rate Lorenz Curve Support Point Discontinuity Point Natural Vector 
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  1. Borzadaran GRM, Behdani Z (2008) Notes Due to Lorenz Curve and Lorenz Ordering in View of Weighted Distributions, 374–386, Proceedings of the 9th Iranian Statistical Conference, Department of Statistics, University of IsfahanGoogle Scholar
  2. Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, New YorkGoogle Scholar

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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