scholarly journals A New Logit-Based Gini Coefficient

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 488
Author(s):  
Hang K. Ryu ◽  
Daniel J. Slottje ◽  
Hyeok Y. Kwon
Keyword(s):  
Distribution Function ◽  
Income Distribution ◽  
Gini Coefficient ◽  
Empirical Distribution Function ◽  
Extreme Values ◽  
Empirical Distribution ◽  
Inequality Measure ◽  
The Gini Coefficient

The Gini coefficient is generally used to measure and summarize inequality over the entire income distribution function (IDF). Unfortunately, it is widely held that the Gini does not detect changes in the tails of the IDF particularly well. This paper introduces a new inequality measure that summarizes inequality well over the middle of the IDF and the tails simultaneously. We adopt an unconventional approach to measure inequality, as will be explained below, that better captures the level of inequality across the entire empirical distribution function, including in the extreme values at the tails.

scholarly journals Nonparametric Estimation of Multivariate Extreme Value Copulas with Known and Unknown Marginal Distributions

2021 ◽  
Vol 2068 (1) ◽  
pp. 012003
Author(s):  
Ayari Samia ◽  
Mohamed Boutahar
Keyword(s):  
Distribution Function ◽  
Empirical Distribution Function ◽  
Extreme Values ◽  
Empirical Distribution ◽  
Extreme Value ◽  
Dependence Function ◽  
Marginal Distributions ◽  
Nonparametric Estimators ◽  
Monte Carlo Experiments ◽  
Multivariate Extreme Values

Abstract The purpose of this paper is estimating the dependence function of multivariate extreme values copulas. Different nonparametric estimators are developed in the literature assuming that marginal distributions are known. However, this assumption is unrealistic in practice. To overcome the drawbacks of these estimators, we substituted the extreme value marginal distribution by the empirical distribution function. Monte Carlo experiments are carried out to compare the performance of the Pickands, Deheuvels, Hall-Tajvidi, Zhang and Gudendorf-Segers estimators. Empirical results showed that the empirical distribution function improved the estimators’ performance for different sample sizes.

Anything Lorenz Curves Can Do, Top Shares Can Do: Assessing the TopBot Family of Inequality Measures

2018 ◽  
Vol 49 (4) ◽  
pp. 947-981 ◽  
Author(s):  
Guillermina Jasso
Keyword(s):  
Gini Coefficient ◽  
Probability Distributions ◽  
The United States ◽  
Current Evidence ◽  
Inequality Measure ◽  
Lorenz Curves ◽  
Inequality Measures ◽  
Top Incomes ◽  
The Gini Coefficient ◽  
And Shifts

Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this article strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single inequality measure, here called TopBot. Second, it presents two standard forms of TopBot, which satisfy the principle of normalization. Third, it presents a new link between top shares and the Gini coefficient, showing that properties and results associated with the Lorenz curve pertain as well to top shares. Fourth, it investigates TopBot in mathematically specified probability distributions, showing that TopBot is monotonically related to classical measures such as the Gini, Atkinson, and Theil measures and the coefficient of variation. Thus, TopBot appears to be a genuine inequality measure. Moreover, TopBot is further distinguished by its ease of calculation and ease of interpretation, making it an appealing People’s measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations and that weakening of correlations signals differences and shifts in distributional form, themselves signals of income dynamics.

Semiparametric estimation and inference

2019 ◽  
pp. 139-164
Author(s):  
M. D. Edge
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Permutation Test ◽  
Cumulative Distribution ◽  
Permutation Testing ◽  
Unknown Distribution ◽  
Regression Parameters ◽  
Independent Observations

Nonparametric and semiparametric statistical methods assume models whose properties cannot be described by a finite number of parameters. For example, a linear regression model that assumes that the disturbances are independent draws from an unknown distribution is semiparametric—it includes the intercept and slope as regression parameters but has a nonparametric part, the unknown distribution of the disturbances. Nonparametric and semiparametric methods focus on the empirical distribution function, which, assuming that the data are really independent observations from the same distribution, is a consistent estimator of the true cumulative distribution function. In this chapter, with plug-in estimation and the method of moments, functionals or parameters are estimated by treating the empirical distribution function as if it were the true cumulative distribution function. Such estimators are consistent. To understand the variation of point estimates, bootstrapping is used to resample from the empirical distribution function. For hypothesis testing, one can either use a bootstrap-based confidence interval or conduct a permutation test, which can be designed to test null hypotheses of independence or exchangeability. Resampling methods—including bootstrapping and permutation testing—are flexible and easy to implement with a little programming expertise.

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