Gini index needs auto-calibration for consistent decision-making.
problem Gini index's inconsistency in decision-making.
method Restrict Gini index to auto-calibrated regression models.
result Gini index becomes strictly consistent with auto-calibration.
Analytical results bound the approach to oligarchy in a modified asset exchange model.
problem Analyzing economic inequality in a modified asset exchange model.
method Analytical results using Gini coefficient and differential inequalities.
result The Gini coefficient is bounded by a first-order differential inequality.
The paper examines stochastic ordering of Gini indexes for multivariate elliptical risks.
problem Stochastic ordering of Gini indexes for multivariate elliptical risks.
method Established conditions for monotonicity of Gini index in usual stochastic order.
result Suitable conditions for multivariate elliptical risks generalize those for multivariate normal risks.
The paper examines the stability of binary choice models using Gini index and scoring indicators.
problem Stability and discriminatory power of binary choice models.
method Derives the real Gini index and incorporates PSI and KS statistics into the model.
result The real Gini index should be less than the calculated Gini index when the population distribution changes.
Study reveals structural constraints on income inequality in Latin America.
problem Income inequality in Latin America compared to other economies.
method Product space, Product Gini Index, Xgini coefficient.
result LAC economies are more dependent on products related to high income inequality.
We propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution which is a good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the…
Paper proves convergence of Gini index to equilibrium in Wasserstein distance.
problem Proving convergence of Gini index to equilibrium in Wasserstein distance.
method Analyzes Gini index as Lyapunov functional and proves convergence in Wasserstein distance.
result Proves convergence of Gini index to equilibrium in Wasserstein distance.
Novel method for multiclass ROC curves using multidimensional Gini index.
problem Multiclass performance evaluation, especially for imbalanced datasets.
method Extends ROC curve methodology to multiclass settings using multidimensional Gini index.
result Validated through case studies in health care and finance.
Paper introduces a new measure combining entropy and Gini index.
problem Quantifying complexity in socio- and econo-physics.
method Generalizes entropy using Gini index and Lorenz curve transformation.
result Supports quantifying complexity in socio- and econo-physics.
Study on Gini estimation for fat-tailed data, showing bias and proposing corrections.
problem Estimating Gini index under infinite variance data.
method Analysis of nonparametric and maximum likelihood estimators, focusing on phase transitions and tail index effects.
result Maximum likelihood estimation outperforms nonparametric methods for fat-tailed data.
Punctuated Equilibrium (PE) states that after long periods of evolutionary quiescence, species evolution can take place in short time intervals, where sudden differentiation makes new species emerge and some species extinct. In this paper, we introduce and study the effect of punctuated equilibrium on two different ass…
Socio-economic inequality is characterized from data using various indices. The Gini (g) index, giving the overall inequality is the most common one, while the recently introduced Kolkata (k) index gives a measure of 1−k fraction of population who possess top k fraction of wealth in the society. Here, we show t…
A new metric assesses spatio-temporal forecast quality using Gini regularized Optimal Transport.
problem Evaluating the quality of spatio-temporal forecasts.
method Gini-regularized Optimal Transport (OT) problem, using Gini impurity function as a regularizer.
result The Gini regularized OT problem converges to the classical OT problem, offering a numerically more stable algorithm.
The paper covers the new model of wage distribution in typical group of people. The model provides the opportunity to reparameterize applicable income distribution model: Pareto, logarithmically normal, logarithmically logistic, Dagum etc. The model ensures the graduation of Gini index values by polynomial degree of wa…
This study examines socio-economic inequality and proposes an international institution to address it.
problem Measuring and understanding socio-economic inequality.
method Analysis of various inequality indices, data sources, and toy models.
result Relationship between Gini and Kolkata indices, insights from natural and social conflicts.
Sparse molecular representations improve interpretability in graph neural networks.
problem Difficulty in understanding which molecular graph aspects drive deep learning predictions.
method Constrain weights in a graph convolutional neural network using the Gini index to maximize representation inequality.
result The Gini-constrained approach does not degrade evaluation metrics and allows for interpretable representation combination.
Survey of κ-generalized models for income and wealth distributions.
problem Analyzing and modeling income and wealth distributions.
method Review of analytical properties, interrelations with other distributions, and empirical applications.
result The κ-generalized models agree well with empirical data. We study the effect of altruism in two simple asset exchange models: the yard sale model (winner gets a random fraction of the poorer player's wealth) and the theft and fraud model (winner gets a random fraction of the loser's wealth). We also introduce in these models the concept of bargaining efficiency, which makes …
In this paper, we study the inequality indices for some models of wealth exchange. We calculated Gini index and newly introduced k-index and compare the results with reported empirical data available for different countries. We have found lower and upper bounds for the indices and discuss the efficiencies of the models…
The construction of efficient and effective decision trees remains a key topic in machine learning because of their simplicity and flexibility. A lot of heuristic algorithms have been proposed to construct near-optimal decision trees. ID3, C4.5 and CART are classical decision tree algorithms and the split criteria they…
Wealth redistribution through Fokker-Planck equation controls preserves Gini coefficient.
problem Preserving Gini coefficient through proportional wealth tax.
method Formulating optimal redistribution as a control problem for Fokker-Planck equation.
result Progressive taxes redistribute within policy-relevant timescales.
Data science reveals co-evolution of income inequality and savings across countries.
problem Understanding the co-evolution of income inequality and savings across countries.
method Time series data for Gini indices and Gross Domestic Savings (% of GDP) were used to construct correlation and similarity matrices, and a multi-dimensional scaling technique was applied. Linear regression was used to test the empirical linkage between income inequality and savings.
result The empirical model proposed by Chakraborti-Chakrabarti (2000) holds reasonably true for many economies of the world, showing a moderate relationship between income inequality and savings.
The paper analyzes ESS metrics and their connections to entropy families.
problem Improving the accuracy of effective sample size approximations.
method Examined Rényi and Tsallis entropy families and their relationship to ESS.
result Proved that ESS functions in the Huggins-Roy family meet theoretical conditions.
New Gini indices capture more nuanced income inequality.
problem Measuring joint dispersion across multiple observations.
method Axiomatic approach to define and characterize n-th order Gini deviations.
result Higher-order Gini coefficients reveal more extreme income disparities.
Paper introduces new metrics for evaluating model accuracy.
problem Improving model accuracy and calibration.
method Developed two second-order accuracy metrics with integral and numerical representations.
result Validates model calibration settings and reveals distortions.
Paper proposes Gini distance statistics for estimating feature-label dependence.
problem Identifying statistical dependence between features and categorical labels.
method Generalized Gini distance in RKHS for feature-label dependence estimation.
result Gini distance statistics converge faster and have tighter error bounds than distance covariance.
Paper discusses extending Gini score for tied rankings and case weights.
problem Extending Gini score for tied rankings and case weights.
method Discuss and adapt Gini score for ties and case weights.
result Gini score can be used for tied rankings and case weights.
New models reduce regional inequality by adjusting exchange range and asset distribution bias.
problem Reduction of regional inequality in economic systems.
method Proposed new asset exchange models with spatial exchange range and local support bias to adjust asset distribution and circulation rates.
result Achieved asset distribution from over-concentration to exponential and eventually normal, reducing Gini coefficient.
Models analyze how different levels of tax evasion affect income distribution.
problem Effects of varying levels of tax evasion on income distribution.
method Microscopic models of economic interactions with a tax system and redistribution.
result Gini inequality index increases with higher evasion levels, but evasion spread does not significantly affect it.
Proposes a simple solution to Gini importance bias in random forests.
problem Gini importance measure in random forests is biased and unreliable.
method Computes loss reduction on out-of-bag samples instead of in-bag.
result Solves the misleading/untrustworthy Gini importance issue.
The evolution of Gini coefficient for personal incomes in the USA between 1947 and 2005 is analyzed and modeled. There are several versions of personal income distribution (PID) provided by the US Census Bureau (US CB) for this period with various levels of resolution. Effectively, these PIDs result in different Gini c…
Paper introduces a new risk measure that considers risk aversion.
problem Risk management and variability assessment.
method Extended Gini Shortfall risk measure using Choquet integral representations.
result The new risk measure is coherent and captures variability.
Paper proposes a fair stock trading strategy using multi-agent reinforcement learning.
problem Unfair stock trading strategies lead to long-term losses for companies.
method Multi-agent reinforcement learning system to balance revenue and fairness.
result The system optimizes individual revenue while maintaining fairness.
Systematizes blockchain decentralization taxonomy and metrics.
problem Lack of a unified definition for blockchain decentralization.
method Formulated a taxonomy of five facets and developed metrics.
result Provided comprehensive insights into blockchain decentralization.
The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.
problem Analyzing worst-case distortion risk metrics and weighted entropy with limited information.
method General distributions, partial information (mean and variance), various entropies and risk measures.
result Provides worst-case results for distortion risk metrics and weighted entropy.
Direct measurements of Gini coefficients by conventional arithmetic calculations are a poor estimator, even if paradoxically, they include the entire population, as because of super-additivity they cannot lend themselves to comparisons between units of different size, and intertemporal analyses are vitiated by the popu…
Binary choice forests model customer choices in retailing.
problem Estimating DCMs using transaction data is challenging and prone to misspecification.
method Random forest of binary decision trees to represent DCMs, interpretable and consistent predictions.
result Random forest can predict choice probabilities and assortments unseen in training data.
We analyze a conservative market model for the competition among economic agents in a close society. A minimum dynamics ensures that the poorest agent has a chance to improve its economic welfare. After a transient, the system self-organizes into a critical state where the wealth distribution have a minimum threshold, …
Two regularization techniques improve GCNN explainability and preference from chemists.
problem Difficulty in rationalizing molecular graph neural network predictions.
method Batch Representation Orthonormalization (BRO) and Gini regularization applied during GCNN training.
result Regularization improves GCNN attribution methods and preference from chemists.
Study on decentralization in DAOs and its effect on financial efficiency in DeFi.
problem Understanding the impact of decentralization on financial efficiency in blockchain-based governance.
method Analysis using Gini coefficient as an inequality indicator, comparing ROI of token owners.
result Real decentralization affects financial efficiency positively in DeFi.
The standard deviation and Gini mean difference order based on tail behavior.
problem Ordering between standard deviation and Gini mean difference for real-valued risks.
method Analysis of the mean excess function of the pairwise difference ∣X−X′∣. result Dominance regimes of SD and GMD are determined by tail behavior of the distribution.
This paper fills in local bounds for Spearman's footrule and Gini's gamma measures of association.
problem Local bounds for bivariate copulas with respect to Spearman's footrule and Gini's gamma measures.
method Computing quasi-copulas that are not copulas for certain values of the measures.
result Presented local bounds for Spearman's footrule and Gini's gamma measures.
Absolute index theorem for warped product manifolds.
problem Equivariant index computation for manifolds with warped product structures.
method Warped product structure, Fredholm operator, Atiyah-Segal-Singer index theorem.
result Equivariant relative index theorem for manifolds with warped product structures.
The argument that the alarming level of Gini coefficient is 0.4 is very popular, especially in the media industry, all around the world for a long time. Although the 0.4 standard is widely accepted, the derivation of the value lacks rigid theoretical foundations. In fact, to the best of our knowledge, it is not based o…
We present a model in which we investigate the structure and evolution of a random network that connects agents capable of exchanging wealth. Economic interactions between neighbors can occur only if the difference between their wealth is less than a threshold value that defines the width of the economic classes. If th…
The study shows products of certain polyhedra have a bounded index property.
problem Understanding the bounded index property for products of polyhedra.
method Analyzing sufficient conditions for the bounded index property in products of polyhedra.
result Products of closed Riemannian manifolds with negative sectional curvature have the bounded index property.
Proves rigidity in product spaces using index theory.
problem Scalar curvature rigidity in product spaces.
method Fredholm family index theorem.
result Recover corresponding results of Clifford-linear index theory.
We define generalized Atiyah-Patodi-Singer boundary conditions of product type for Dirac operators associated to C*-vector bundles on the product of a compact manifold with boundary and a closed manifold. We prove a product formula for the K-theoretic index classes, which we use to generalize the product formula for th…