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.

(2024). Gini-stable Lorenz curves and their relation to the generalised Pareto distribution [journal article - articolo]. In JOURNAL OF INFORMETRICS. Retrieved from https://hdl.handle.net/10446/262852

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

Bertoli-Barsotti, Lucio;
2024-01-15

Abstract

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.
articolo
15-gen-2024
BERTOLI BARSOTTI, Lucio; Gagolewski, Marek; Siudem, Grzegorz; Żogała-Siudem, Barbara
(2024). Gini-stable Lorenz curves and their relation to the generalised Pareto distribution [journal article - articolo]. In JOURNAL OF INFORMETRICS. Retrieved from https://hdl.handle.net/10446/262852
File allegato/i alla scheda:
File Dimensione del file Formato  
LBB et al 2024 - Gini-stable Lorenz curves and their relation to the generalised Pareto distribution.pdf

accesso aperto

Versione: publisher's version - versione editoriale
Licenza: Creative commons
Dimensione del file 928.72 kB
Formato Adobe PDF
928.72 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Aisberg ©2008 Servizi bibliotecari, Università degli studi di Bergamo | Terms of use/Condizioni di utilizzo

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/262852
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact