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.
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.
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.
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 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.
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.
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…
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.
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.
Investigates relationships between concordance measures and non-exchangeability in copulas.
problem Understanding the relationship between concordance measures and non-exchangeability in copulas.
method Examines five concordance measures (Spearman's rho, Kendall's tau, Gini's gamma, Blomqvist's beta, and footrule) and their connection to non-exchangeability in copulas.
result New method proposed for exploring the relationship between copula properties and measures of dependence.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
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…
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.
Study examines Blomqvist's beta and four concordance measures on copulas.
problem Relating Blomqvist's beta to other concordance measures.
method Estimating concordance measures on copulas with fixed beta.
result Novel method for estimating concordance measures.
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.
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.
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.
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.
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 article compares predictor importance in classification problems with categorical outcomes.
problem Comparing predictor importance in classification problems with categorical response variables.
method The approach is based on the categorical Gini correlation (CGC) and tests differences in CGCs across predictor groups.
result The proposed methodology accommodates predictors of arbitrary and unequal dimensions and allows for dependence between predictor groups.
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.
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.
Framework monitors insurance pricing models for drift and recalibration.
problem Maintaining predictive performance of pricing models in evolving insurance portfolios.
method Formalizes deviance loss and Murphy's score, studies Gini score, develops monitoring framework.
result Framework guides decisions on refitting or recalibrating pricing models.
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.
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…
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.
We consider concepts and models for measuring inequality in the distribution of resources with a focus on how inequality varies as a function of covariates. Lorenz introduced a device for measuring inequality in the distribution of income that indicates how much the incomes below the uth quantile fall short of the…
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.
The paper explores optimal insurance contracts using various deviation measures.
problem Optimal insurance contracts with mean-deviation measures.
method Study of convex signed Choquet integrals and standard deviation as deviation measures, analyzing premium principles like expected value, Value-at-Risk, and Expected Shortfall.
result Characterization of optimal indemnities and deductibles under different premium principles.
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.
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…
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…
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 curve and the Gini coefficient - are given. A method for parameter estimation is …
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…
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…
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.
The CAP slope is Bayes' theorem in cumulative coordinates, unlocking the weight of evidence, Somers' D, and Gini coefficient.
problem Calibration and weight of evidence
method Identifying the CAP slope as Bayes' theorem
result Revealing the CAP slope as Bayes' theorem
Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families wi…
In recent work, Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy -- complete concentration of wealth by a single …
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.
Study measures inequality in social-economic systems using Fokker-Planck equations and Lotka-Volterra dynamics.
problem Measuring inequality in oscillatory social-economic systems described by Fokker-Planck equations and Lotka-Volterra dynamics.
method Used Fokker-Planck equations and Lotka-Volterra dynamics to model inequality, focusing on coefficient of variation as a measure.
result Inequality initially tends to decrease in oscillatory systems, contrary to steady-state models.
Socio-economic inequality is measured using various indices. The Gini (g) index, giving the overall inequality is the most commonly used, 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. This article reviews the ch…
The paper addresses risk sharing and variability measures among agents with general risk preferences.
problem Risk sharing and variability measures among agents with general risk preferences.
method Characterizes Pareto-optimal allocations using Gini deviation, mean-median deviation, and inter-quantile difference as variability measures.
result Optimal allocations are not comonotonic and feature a mixture of pairwise counter-monotonic structures.
Unified view of improving tree model interpretability and debiasing feature importance.
problem Improving interpretability and debiasing feature importance in tree-based models.
method Demonstrates a common thread among bias correction methods and local explanations for trees.
result Points out a bias in explainable AI for trees algorithms due to inbag data inclusion.
A microeconomic model is developed, which accurately predicts the shape of personal income distribution (PID) in the United States and the evolution of the shape over time. The underlying concept is borrowed from geo-mechanics and thus can be considered as mechanics of income distribution. The model allows the resoluti…
SAERMA combines deep learning and rule mining to identify SNP interactions.
problem Identifying significant SNPs and their interactions in complex diseases.
method Stacked Autoencoder Rule Mining Algorithm (SAERMA) integrating deep learning and association rule mining.
result Achieved high classification accuracy (77% AUC, 77% SE, 68% SP) with 100 units.
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…