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

TL;DR

This paper explores the relationship between skewness and kurtosis in economic and demographic data, revealing links to growth models based on preferential attachment, with implications for understanding underlying distributional structures.

Contribution

It introduces a method to infer structural parameters of data distributions from high-order moments, connecting skewness and kurtosis to growth models like the Beta and Yule-Simon distributions.

Findings

Skewness-kurtosis relations indicate underlying distribution parameters.

Rank-size analysis reveals parameters of Beta and Yule-Simon models.

Preferential attachment processes are suggested as growth mechanisms.

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.