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.

k-generalized statistics in personal income distribution

CLEMENTI, FABIO;
2007-01-01

Abstract

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.
2007
Les Ulis: EDP Sciences. 2000- Springer Verlag Germany:Tiergartenstrasse 17, D 69121 Heidelberg Germany:011 49 6221 3450, EMAIL: g.braun@springer.de, INTERNET: http://www.springer.de, Fax: 011 49 6221 345229
Internazionale
http://www.springerlink.com/content/e350676km2331578/
File in questo prodotto:
File Dimensione Formato  
fulltext.pdf

solo utenti autorizzati

Tipologia: Documento in post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: DRM non definito
Dimensione 754.12 kB
Formato Adobe PDF
754.12 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11393/38107
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 55
  • ???jsp.display-item.citation.isi??? 54
social impact