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

• Published in: arXiv.org
• Main Authors: Adams Vallejos, Ormazabal, Ignacio, Borotto, Felix A, Astudillo, Hernan F
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 17.05.2018
• Subjects: Deformation; Exchanging; Mathematical models; Parameters; Particle size distribution; Power law; Probability distribution functions; Statistical analysis; Wealth distribution
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1805.06929

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.