Artículo

Gini-stable Lorenz curves and their relation to the generalised Pareto distribution

Resumen

We introduce an iterative discrete information production process where we can extend ordered normalised vectors by new elements based on a simple affine transformation, while preserving the predefined level of inequality, G, as measured by the Gini index. Then, we derive the family of empirical Lorenz curves of the corresponding vectors and prove that it is stochastically ordered with respect to both the sample size and G which plays the role of the uncertainty parameter. We prove that asymptotically, we obtain all, and only, Lorenz curves generated by a new, intuitive parametrisation of the finite-mean Pickands’ Generalised Pareto Distribution (GPD) that unifies three other families, namely: the Pareto Type II, exponential, and scaled beta distributions. The family is not only totally ordered with respect to the parameter G, but also, thanks to our derivations, has a nice underlying interpretation. Our result may thus shed a new light on the genesis of this family of distributions. Our model fits bibliometric, informetric, socioeconomic, and environmental data reasonably well. It is quite user-friendly for it only depends on the sample size and its Gini index.
Liu, Getong (59384702500); Sun, Jiajun (57205440975); Liu, Chenfeng (57221207978); Shi, Huading (14032147800); Fei, Yang (57193509358); Wang, Chen (57876636400); Zhang, Guilong (58736127100); Wang, Hongjie (57210435095)
Progress and Trends in Research on Soil Nitrogen Leaching: A Bibliometric Analysis from 2003 to 2023
2025
10.3390/su17010339
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85214452672&doi=10.3390%2fsu17010339&partnerID=40&md5=dd8623e75ddb80512caa0b4ea6db1af7
Technical Centre for Soil, Agriculture and Rural Ecology and Environment, Ministry of Ecology and Environment, Beijing, 100012, China; Hebei Key Laboratory of Close-to-Nature Restoration Technology of Wetlands, School of Eco-Environment, Hebei University, Baoding, 071002, China; Agro-Environmental Protection Institute, Ministry of Agriculture and Rural Affairs, Tianjin, 300000, China; Engineering Research Center of Ecological Safety and Conservation in Beijing-Tianjin-Hebei (Xiong’an New Area) of MOE, Baoding, 071002, China
All Open Access; Gold Open Access
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