A new $\kappa$-deformed parametric model for the size distribution of wealth

Abstract

It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions corresponding to particular subsets of agents. Here, we propose a new four-parameter statistical distribution which is a $\kappa$-deformation of the Generalized Gamma distribution with a power-law tail, based on the deformed exponential and logarithm functions introduced by Kaniadakis(2001). We found that this new distribution is also an extension to the $\kappa$-Generalized distribution proposed by Clementi et al. (2007), with an additional shape parameter $\nu$, and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models. We also provide various associated statistical measures and inequality measures.

References in corpus (22)

• Power-law distributions in empirical data
• Power laws, Pareto distributions and Zipf's law
• 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 of money
• Statistical mechanics of money: How saving propensity affects its distribution
• Statistical mechanics in the context of special relativity II
• Evidence for the exponential distribution of income in the USA
• Pareto Law in a Kinetic Model of Market with Random Saving Propensity
• Economic Fluctuations and Diffusion
• A statistical model with a standard Gamma distribution
• Distributions of money in model markets of economy
• Theoretical foundations and mathematical formalism of the power-law tailed statistical distributions
• Maximum entropy principle and power-law tailed distributions
• Dynamics of Money and Income Distributions
• Master equation for a kinetic model of trading market and its analytic solution
• Money in Gas-Like Markets: Gibbs and Pareto Laws
• Influence of saving propensity on the power law tail of wealth distribution
• Kinetic theory models for the distribution of wealth: power law from overlap of exponentials
• Gamma-distribution and wealth inequality
• A distribution function analysis of wealth distribution

Cited by in corpus (2)

• The k-statistics approach to epidemiology
• New power-law tailed distributions emerging in $\kappa$-statistics