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.
Bertoli-Barsotti, Lucio (9840093000); Gagolewski, Marek (55971798100); Siudem, Grzegorz (36773883100); Żogała-Siudem, Barbara (56563026400)
Gini-stable Lorenz curves and their relation to the generalised Pareto distribution
2024
10.1016/j.joi.2024.101499
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85182393140&doi=10.1016%2fj.joi.2024.101499&partnerID=40&md5=71ceb45c2abdf3048bd351cadd1d4af9
University of Bergamo, Department of Economics, Italy; Deakin University, Data to Intelligence Research Centre, School of IT, Geelong, 3220, VIC, Australia; Warsaw University of Technology, Faculty of Mathematics and Information Science, ul. Koszykowa 75, Warsaw, 00-662, Poland; Warsaw University of Technology, Faculty of Physics, ul. Koszykowa 75, Warsaw, 00-662, Poland; Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, Warsaw, 01-447, Poland
All Open Access; Green Open Access; Hybrid Gold Open Access
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