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We consider Gini's mean difference statistic as an alternative to the empirical variance in the settings of finite populations where simple random samples are drawn without replacement. In particular, we discuss specific (in the finite…

Statistics Theory · Mathematics 2014-06-10 Andrius Čiginas , Dalius Pumputis

This paper deals with fairness in stable marriage problems. The idea studied here is to achieve fairness thanks to a Generalized Gini Index (GGI), a well-known criterion in inequality measurement, that includes both the egalitarian and…

Computational Complexity · Computer Science 2018-09-25 Hugo Gilbert , Olivier Spanjaard

We study the effect of the social stratification on the wealth distribution on a system of interacting economic agents that are constrained to interact only within their own economic class. The economical mobility of the agents is related…

Physics and Society · Physics 2009-11-11 M. F. Laguna , S. Risau Gusman , J. R. Iglesias

The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to…

Populations and Evolution · Quantitative Biology 2022-09-28 José Manuel Aburto , Ugofilippo Basellini , Annette Baudisch , Francisco Villavicencio

Wealth distribution is a complex and critical aspect of any society. Information exchange is considered to have played a role in shaping wealth distribution patterns, but the specific dynamic mechanism is still unclear. In this research, we…

Computer Vision and Pattern Recognition · Computer Science 2023-04-04 Yang Shao , Hirokazu Atsumori , Tadayuki Matsumura , Kanako Esaki , Shunsuke Minusa , Hiroyuki Mizuno

We introduce the social welfare implications of the Zenga index, a recently proposed index of inequality. Our proposal is derived by following the seminal book by Son (2011) and the recent working paper by Kakwani and Son (2019). We compare…

General Economics · Economics 2020-06-24 Francesca Greselin , Simone Pellegrino , Achille Vernizzi

This paper proposes a new Bayesian approach to estimate the Gini coefficient from the Lorenz curve based on grouped data. The proposed approach assumes a hypothetical income distribution and estimates the parameter by directly working on…

Applications · Statistics 2017-08-10 Genya Kobayashi , Kazuhiko Kakamu

This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost…

Methodology · Statistics 2017-09-21 Shyamal Krishna De , Bhargab Chattopadhyay

We propose a new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson $R^2$ in ANOVA model, the Gini correlation is interpreted as the ratio of the between-group variation and the total…

Methodology · Statistics 2019-07-10 Xin Dang , Dao Nguyen , Yixin Chen , Junying Zhang

In this paper, we obtain an upper bound for the Gini mean difference based on mean, variance and correlation for the case when the variables are correlated. We also derive some closed-form expressions for the Gini mean difference when the…

Statistics Theory · Mathematics 2023-01-20 Roberto Vila , Narayanaswamy Balakrishnan , Helton Saulo

Income inequality measures are often used as an indication of economic health. How to obtain reliable confidence intervals for these measures based on sampled data has been studied extensively in recent years. To preserve confidentiality,…

Applications · Statistics 2019-07-22 Dilanka S. Dedduwakumara , Luke A. Prendergast

This paper proposes the k-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement - such as the Lorenz…

General Finance · Quantitative Finance 2009-01-31 F. Clementi , T. Di Matteo , M. Gallegati , G. Kaniadakis

This paper aims to review the different impacts of income inequality drivers on the Gini coefficient, depending on institutional specificities. In this context, we divided the European Union member states in two clusters (the cluster of…

We introduce two families of inequality measures, $G_p$ and $H_q$, that converge to the classical Gini coefficient as $p,q\to\infty$. The tuning parameters $p>1$ and $q>0$ regulate the influence of disparities between observations. For each…

Methodology · Statistics 2026-05-11 Roberto Vila , Helton Saulo

Inequality indices are quantitative scores that gauge the divergence of wealth distributions in human societies from the "ground state" of pure communism. While inequality indices were devised for socioeconomic applications, they are…

Statistical Mechanics · Physics 2017-03-31 I. Eliazar

Crime is an economically important activity, sometimes called the industry of crime. It may represent a mechanism of wealth distribution but also a social and economic charge because of the cost of the law enforcement system. Sometimes it…

Adaptation and Self-Organizing Systems · Physics 2007-10-22 Mirta B. Gordon , J. R. Iglesias , Viktoriya Semeshenko , J. -P. Nadal

To demonstrate the usefulness of physical approaches for the study of realistic economic systems, we investigate the inequality of players' wealth in one of the most extensively studied econophysical models, namely, the minority game (MG).…

Statistical Mechanics · Physics 2009-11-10 K. H. Ho , F. K. Chow , H. F. Chau

Via an axiomatic approach, we characterize the family of n-th order Gini deviation, defined as the expected range over n independent draws from a distribution, to quantify joint dispersion across multiple observations. This family extends…

Mathematical Finance · Quantitative Finance 2025-09-16 Xia Han , Ruodu Wang , Qinyu Wu

Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between two multivariate distributions, we introduce a new measure…

Methodology · Statistics 2024-11-05 Gennaro Auricchio , Giovanni Brigati , Paolo Giudici , Giuseppe Toscani

Composite indices like the Gender Equality Index (GEI) are widely used to monitor gender disparities and guide evidence-based policy. However, their original design is often limited when applied to subnational contexts. Building on the GEI…

Applications · Statistics 2026-01-21 Lorenzo Panebianco