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

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  • Adams Vallejos
  • Ignacio Ormazabal
  • Felix A. Borotto
  • Hernan F. Astudillo

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.

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  • Adams Vallejos & Ignacio Ormazabal & Felix A. Borotto & Hernan F. Astudillo, 2018. "A new $\kappa$-deformed parametric model for the size distribution of wealth," Papers 1805.06929, arXiv.org.
    • Handle: RePEc:arx:papers:1805.06929
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    References listed on IDEAS

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