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Tsallis Statistics in the Income Distribution of Brazil

A. D. Soares, N. J. Moura Jr & Marcelo B. Ribeiro

posted on 23 November 2019

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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.


The results show that Brazil’s complementary cumulative income distribution can be linearized by the q-logarithm and fitted by using only two parameters. For Brazil q ranges from 1.19 to 1.54 and fluctuates with a period of approximately 3.5 years. Both fitted parameters also present a cycling behavior in terms of one another.