Eur. Phys. J. B 57, 187-193 (2007)
https://doi.org/10.1140/epjb/e2007-00120-9

κ-generalized statistics in personal income distribution

¹ Department of Economics, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy
² Department of Physics, Polytechnic University of Turin, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Corresponding author: ^a fabio.clementi@univpm.it

Received: 31 August 2006
Revised: 22 February 2007
Published online: 11 May 2007

Abstract

Starting from the generalized exponential function , with exp ₀(x)=exp (x), proposed in reference [G. Kaniadakis, Physica A 296, 405 (2001)], the survival function P_>(x)=exp _κ(-βx^α), where x∈R⁺, α,β>0, and , 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 (-βx^α) 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.