Gini-stable Lorenz curves and their relation to the generalised Pareto distribution 2024

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.

Autores	Pedraja-Rejas, L; Rodriguez-Ponce, E; Munoz-Fritis, C; Laroze, D
Título	Sustainable Development Goals and Education: A Bibliometric Review-The Case of Latin America
Afiliaciones	Universidad de Tarapaca; Universidad de Tarapaca
Año	2023
DOI	10.3390/su15129833
Tipo de acceso abierto	gold
Referencia	WOS:001015693100001
Artículo obtenido de:	WOS

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

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