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

Abstract

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 concerns 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.