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

TL;DR

This paper introduces a novel four-parameter $ppa$-deformed distribution for modeling wealth distribution, extending previous models with enhanced flexibility and accurately capturing the entire wealth spectrum in kinetic exchange models.

Contribution

It proposes a new $ppa$-deformed distribution extending the $ppa$-Generalized distribution with an extra shape parameter, improving modeling of wealth distributions.

Findings

The distribution accurately models wealth in heterogeneous kinetic exchange models.

It generalizes previous $ppa$-distributions with additional parameters.

Provides statistical and inequality measures for the new distribution.

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.