The European Physical Journal B

, Volume 57, Issue 2, pp 187–193 | Cite as

κ-generalized statistics in personal income distribution

  • F. ClementiEmail author
  • M. Gallegati
  • G. Kaniadakis
Topical Issue on Physics in Society


Starting from the generalized exponential function \(\exp_{\kappa}(x)=(\sqrt{1+\kappa^{2}x^{2}}+\kappa x)^{1/\kappa}\), with exp 0(x)=exp (x), proposed in reference [G. Kaniadakis, Physica A 296, 405 (2001)], the survival function P>(x)=exp κ(-βxα), where x∈R+, α,β>0, and \(\kappa\in[0,1)\), is considered in order to analyze the data on personal income distribution for Germany, Italy, and the United Kingdom. The above defined distribution is a continuous one-parameter deformation of the stretched exponential function P> 0(x)=exp (-βxα) to which reduces as κ approaches zero behaving in very different way in the x→0 and x→∞ regions. Its bulk is very close to the stretched exponential one, whereas its tail decays following the power-law P>(x)∼(2βκ)-1/κx-α/κ. This makes the κ-generalized function particularly suitable to describe simultaneously the income distribution among both the richest part and the vast majority of the population, generally fitting different curves. An excellent agreement is found between our theoretical model and the observational data on personal income over their entire range.


02.50.Ng Distribution theory and Monte Carlo studies 02.60.Ed Interpolation; curve fitting 89.65.Gh Economics; econophysics, financial markets, business and management 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of EconomicsPolytechnic University of MarcheAnconaItaly
  2. 2.Department of PhysicsPolytechnic University of TurinTorinoItaly

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