Intriguing yet simple skewness: kurtosis relation in economic and demographic data distributions, pointing to preferential attachment processes

In this paper, we propose that relations between high-order moments of data distributions, for example, between the skewness (S) and kurtosis (K), allow to point to theoretical models with understandable structural parameters. The illustrative data concern two cases: (i) the distribution of income taxes and (ii) that of inhabitants, after aggregation over each city in each province of Italy in 2011. Moreover, from the rank-size relationship, for either S or K, in both cases, it is shown that one obtains the parameters of the underlying (hypothetical) modeling distribution: in the present cases, the 2-parameter Beta function, itself related to the Yule–Simon distribution function, whence suggesting a growth model based on the preferential attachment process.