Oscillations in the Tsallis income distribution

TL;DR

This paper introduces a novel approach to modeling income distribution oscillations by allowing the Tsallis q-parameter to be complex, successfully capturing the oscillatory behavior in Brazilian income data.

Contribution

It proposes using a complex Tsallis q-parameter to naturally describe oscillations in income distribution, providing a new theoretical framework for analyzing CCDF oscillations.

Findings

Successfully modeled oscillations in Brazilian income data

Recovered main oscillatory features with a non-linear CCDF function

Demonstrated the approach's potential for understanding income distribution dynamics

Abstract

Oscillations in the complementary cumulative distribution function (CCDF) of individual income data have been found in the data of various countries studied by different authors at different time periods, but the dynamical origins of this behavior are currently unknown. Although these datasets can be fitted by different functions at different income ranges, the Tsallis distribution has recently been found capable of fitting the whole distribution by means of only two parameters. This procedure showed clearly such oscillatory feature in the entire income range feature, but made it particularly visible at the tail of the distribution. Although log-periodic functions fitted to the data are capable of describing this behavior, a different approach to naturally disclose such oscillatory characteristics is to allow the Tsallis $q$-parameter to become complex. In this paper we use this idea in order to describe the behavior of the CCDF of the Brazilian personal income recently studied empirically by Soares et al.\ (2016). Typical elements of periodic motion, such as amplitude and angular frequency coupled to this income analysis, were obtained by means of this approach. A highly non-linear function for the CCDF was obtained through this methodology and a numerical test showed it capable of recovering the main oscillatory feature of the original CCDF of the personal income data of Brazil.