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

2017/12/15 by Marcel Ausloos, Roy Cerqueti
Mathematics · Physics and Astronomy · Social Sciences · #Demographic Trends and Gender Preferences #Distribution (mathematics) #Family Dynamics and Relationships #Insurance, Mortality, Demography, Risk Management #Kurtosis #Point (geometry) #Relation (database) #Simple (philosophy) #Skewness #math.ST #physics.soc-ph #stat.AP #stat.TH

paper · pdf · doi:10.1080/02664763.2017.1413077

published as Journal of Applied Statistics, 45:12, 2202-2218 (2018) · 29 pages, 5 tables, 10 figures, 56 references

openalex publication_date 2017/12/15 · openalex created_date 2017/12/22 · arxiv created 2018/07/18 · arxiv updated 2018/07/19 · openalex updated_date 2026/08/05

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 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.

Citations

• Measures of multivariate skewness and kurtosis with applications
• Benford’s law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions
• IX. Mathematical contributions to the theory of evolution.—XIX. Second supplement to a memoir on skew variation