k-Generalized Statistics in Personal Income Distribution

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 Ref. [G. Kaniadakis, Physica A \textbf{296}, 405 (2001)], the survival function $P_{>}(x)={\exp }_{\kappa }(-\beta x^{\alpha })$, where $x\in {\mathbf{R}}^{+}$, $\alpha ,\beta >0$, 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 $P_{>}^0(x)=\exp (-\beta x^{\alpha })$\textemdash to which reduces as $\kappa$ approaches zero\textemdash behaving in very different way in the $x\to 0$ and $x\to \infty$ regions. Its bulk is very close to the stretched exponential one, whereas its tail decays following the power-law $P_{>}(x)\sim (2\beta \kappa {)}^{-1/\kappa }{x}^{-\alpha /\kappa }$. This makes the $\kappa$-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.

Latex2e v1.6; 14 pages with 12 figures; for inclusion in the APFA5 Proceedings

References in corpus (13)

• Stretched exponential distributions in Nature and Economy: ``Fat tails'' with characteristic scales
• Statistical mechanics in the context of special relativity
• Non Linear Kinetics underlying Generalized Statistics
• Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States
• Statistical mechanics in the context of special relativity II
• Evidence for the exponential distribution of income in the USA
• H-Theorem and Generalized Entropies Within the Framework of Non Linear Kinetics
• Power Law Tails in the Italian Personal Income Distribution
• Temporal evolution of the "thermal" and "superthermal" income classes in the USA during 1983-2001
• The Power-law Tail Exponent of Income Distributions
• Towards a relativistic statistical theory
• Exchanges in complex networks: income and wealth distributions
• Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution

Cited by in corpus (28)

• Colloquium: Statistical mechanics of money, wealth, and income
• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Maximum entropy principle and power-law tailed distributions
• The k-generalized distribution: A new descriptive model for the size distribution of incomes
• Relativistic Entropy and Related Boltzmann Kinetics
• The Gompertz-Pareto Income Distribution
• A generalized statistical model for the size distribution of wealth
• Tsallis statistics in the income distribution of Brazil
• $\kappa$-generalized models of income and wealth distributions: A survey
• A k-generalized statistical mechanics approach to income analysis
• Exploiting the flexibility of a family of models for taxation and redistribution
• Behavioral and Network Origins of Wealth Inequality: Insights from a Virtual World
• Income distribution patterns from a complete social security database
• Composition law of $\kappa$-entropy for statistically independent systems
• Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems
• k-Deformed Fourier Transform
• Oscillations in the Tsallis income distribution
• Economic inequality and mobility in kinetic models for social sciences
• Physical origin of the power-law tailed statistical distributions
• Relativistic kinetics and power-law tailed distributions
• Relativistic Roots of $\kappa$-Entropy
• Scaling in Income Inequalities and its Dynamical Origin
• Power-Law tailed statistical distributions and Lorentz transformations
• Inequality, mobility and the financial accumulation process: A computational economic analysis
• Household Income Distribution in the USA
• Econophysics, Statistical Mechanics Approach to
• Modelling income, wealth, and expenditure data by use of Econophysics
• New economic windows on income and wealth: The k-generalized family of distributions