A newκ-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 fourparameter statistical distribution which is a κ-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 κ-Generalized distribution proposed by Clementi et al. (2007), with an additional shape parameter ν, 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.

The κ-statistics approach to epidemiology

“…For this reason, it has attracted the interest of many researchers over the last two decades who have studied its foundations and mathematical aspects 49 – 58 , the underlying thermodynamics 59 , 60 , and specific applications of the theory to various fields. A non-exhaustive list of applications includes those in quantum statistics 61 – 64 , in quantum entanglement 65 , 66 , in plasma physics 67 – 73 , in nuclear fission 74 – 77 , in astrophysics 78 – 81 , in quantum gravity 82 – 87 , in geomechanics 88 , 89 , in genomics 90 , 91 , in complex networks 92 – 94 , in economy 95 – 99 , in finance 100 – 103 , as well as in reliability analysis and seismology 104 – 106 .…”

The Kaniadakis Distribution for the Analysis of Income and Wealth Data

“…The new variants of the -generalized distribution outperform other four-parameter models in almost all cases, especially in estimating inequality indices with greater precision. In addition, a -deformation of the generalized gamma distribution with a power-law tail has recently been proposed by [ 99 ], to which the reader is referred for further details.)…”