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Extreme points of Lorenz and ROC curves with applications to inequality analysis

Author
Baíllo Moreno, Amparountranslated; Cárcamo Urtiaga, Javieruntranslated; Mora Corral, Carlosuntranslated
Entity
UAM. Departamento de Matemáticas
Publisher
Elsevier
Date
2022-10-15
Citation
10.1016/j.jmaa.2022.126335
Journal of Mathematical Analysis and Applications 514.2 (2022): 126335
 
 
 
ISSN
0022-247X (print); 1096-0813 (online)
DOI
10.1016/j.jmaa.2022.126335
Funded by
A. Baíllo and J. Cárcamo are supported by the Spanish MCyT grant PID2019-109387GB-I00. C. MoraCorral is supported by the Spanish MCyT grant MTM2017-85934-C3-2-P
Project
Gobierno de España. PID2019-109387GB-I00; Gobierno de España. MTM2017-85934-C3-2-P
Editor's Version
https://doi.org/10.1016/j.jmaa.2022.126335
Subjects
Lorenz Curve; Decomposition; Inequality Indices; Matemáticas
URI
http://hdl.handle.net/10486/707315
Rights
© 2022 The Authors

Licencia de Creative Commons
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Abstract

We find the extreme points of the set of convex functions ℓ : [0,1] → [0,1] with a fixed area and ℓ(0) = 0, ℓ(1) = 1. This collection is formed by Lorenz curves with a given value of their Gini index. The analogous set of concave functions can be viewed as Receiver Operating Characteristic (ROC) curves. These functions are extensively used in economics (inequality and risk analysis) and machine learning (evaluation of the performance of binary classifiers). We also compute the maximal L1-distance between two Lorenz (or ROC) curves with specified Gini coefficients. This result allows us to introduce a bidimensional index to compare two of such curves, in a more informative and insightful manner than with the usual unidimensional measures considered in the literature (Gini index or area under the ROC curve). The analysis of real income microdata illustrates the practical use of this proposed index in statistical inference
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Google™ Scholar:Baíllo Moreno, Amparo - Cárcamo Urtiaga, Javier - Mora Corral, Carlos

This item appears in the following Collection(s)

  • Producción científica en acceso abierto de la UAM [17185]

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