Tsallis statistics in the income distribution of Brazil

• Tsallis q-exponential is used for describing the personal income data of Brazil from 1978 to 2014.
• The data of the whole distribution is linearized by the q-logarithm and fitted to a straight line.
• A single function with only two parameters is capable of representing the entire distribution.
• The fitted parameters evolve periodically in time and present a mostly clockwise closed cycle in terms of one another.
• A periodic oscillation of the data along the fitted straight line is also observed.

This paper discusses the empirical evidence of Tsallis statistical functions in the personal income distribution of Brazil. Yearly samples from 1978 to 2014 were linearized by the q-logarithm and straight lines were fitted to the entire range of the income data in all samples, producing a two-parameters-only single function representation of the whole distribution in every year. The results showed that the time evolution of the parameters is periodic and plotting one in terms of the other reveals a cycle mostly clockwise. It was also found that the empirical data oscillate periodically around the fitted straight lines with the amplitude growing as the income values increase. Since the entire income data range can be fitted by a single function, this raises questions on previous results claiming that the income distribution is constituted by a well defined two-classes-base income structure, since such a division in two very distinct income classes might not be an intrinsic property of societies, but a consequence of an a priori fitting-choice procedure that may leave aside possibly important income dynamics at the intermediate levels.