• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.283-291
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• 2003

The Gini index is one of the most commonly used measures of inequality of income distributions. In this paper, the Lorenz curve is estimated by arcs of two optimal circles, and a new simple method to estimate the Gini index is proposed using the law of cosines. We compare the proposed estimator with the estimator proposed by Ogwang and Rao(1996) in terms of the mean squared error(MSE) though Monte Carlo simulation in a Pareto distribution.

• Asia-Pacific Journal of Business
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• v.8 no.2
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• pp.15-30
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• 2017

This study analyzes the relationship between income inequality and economic growth. Gini coefficient (market income), the deciles income inequality index and per capita real GDP were analyzed. Furthermore, various cointegration tests were tried to improve the reliability of the test results. From the weak exogeniety test of between per capita real GDP and the Gini coefficient (market income), per capita real GDP has a weak exogeneity while the Gini coefficient is endogenous. From the various cointegration tests, we found out that there is a cointegration between Gini coefficient and per capita real GDP. Moreover, it is estimated that per capita real GDP has a positive effect on the Gini coefficient (market income). In the VAR Granger causal analysis, per capita real GDP affects the Gini coefficient (market income), but it is difficult to say that the Gini coefficient (market income) always has an effect on per capita real GDP. Also, the impulse-response function of the VAR model shows that per capita real GDP temporarily reduces the Gini coefficient (market income), and then increases it over time. Accordingly, it is necessary for the policies to improve not only the distribution structure but also income distribution through economic growth.

• 사회경제평론
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• no.38
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• pp.9-49
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• 2012

Our luck is brute if we cannot choose or control it and, thus, we are not responsible for it. Our luck is optional if we can choose or control it and, thus, we are responsible for it. Egalitarian justice at least demands brute luck be fully neutralized. If, however, brute luck is not fully neutralized and possibly accumulated, what will happen to the Gini coefficients as a measure of inequality due to brute luck? By simulating brute luck under various combinations of the rate of accumulation and the level of, what I call, leximin-redistribution, I obtain the Gini coefficients for the distribution of the accumulated and, then, redistributed brute luck. The level of the leximin-redistribution determines the negative or positive relation between the rate of accumulation and the Gini coefficient. The minimum leximin-redistribution level that generates the negative relation between the rate of accumulation and the Gini coefficient, depends on the characteristics of the starting-point distribution of brute luck. The sooner the leximin-redistribution is ushered in, the lower the minimum level becomes. The so-called 'Growth First Redistribution Later' policy may hurt victims of brute bad luck.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.339-351
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• 2017

Resampling approaches were the first techniques employed to compute a variance for the Gini coefficient; however, many authors have shown that an analysis of the Gini coefficient and its corresponding variance can be obtained from a regression model. Despite the simplicity of the regression approach method to compute a standard error for the Gini coefficient, the use of the proposed regression model has been challenging in economics. Therefore in this paper, we focus on a comparative study among the regression approach and resampling techniques. The regression method is shown to overestimate the standard error of the Gini index. The simulations show that the Gini estimator based on the modified regression model is also consistent and asymptotically normal with less divergence from normal distribution than other resampling techniques.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.121-126
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• 2003

소득분배의 가장 대표적인 불평등척도는 Gini index이며, 이것은 통계학자인 Gini가 제안한 지표로서 소득분배에 관한 분석에서 가장 널리 이용되고 있다. 본 논문에서는 두 원의 호에 의해 Lorenz 곡선을 추정하고 코사인법칙을 이용하여 Gini index를 추정하기 위한 새로운 간편한 방법을 제시하여, 소득분포를 따르는 파레토분포에서 모의실험을 통해 Ogwang and Rao (1996)의 추정방법과 평균제곱오차 면에서 비교 분석한다.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.24 no.67
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• pp.11-18
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• 2001

The efficiency and robustness of the scale estimator based on the Gini's mean difference are well known in Nam et al.(2000). In this paper we propose use of robust control limits based on the Gini's mean difference for the control of the process deviation. To compare the performances of the proposed control chart with the existing R-chart or S-chart, some Monte Carlo simulations are performed. The simulation results show that the use of the Gini's mean difference in construction of the control limits has good performance.

• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.97-103
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• 1995

In this paper, we propose estimators of Gini index of the exponential distribution. We also obtain the distribution and the moments of the proposed estimators. The moments of the proposed estimators are derived by special function. We compare the maximum likelihood estimator (MLE) of Gini index with the proposed estimator of Gini index in the sense of MSE through Monte Carlo Method.

• Journal of Korean Society of Rural Planning
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• v.16 no.2
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• pp.57-64
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• 2010

This study aims to understand the degree of inequality of surveyed amenity resources and identify which resource and region have the highest concentration by estimating Lorenz Curve and the Gini's Coefficient. The Lorenz Curve and Gini's Coefficient derived from economics are introduced as tools for investigating and quantifying regional variability of amenity resources concentration. This study describes the concepts underlying the application of the Gini's coefficient to measure the concentration of amenity resources in 11 regions, Chungbuk Province, Korea. The Lorenz Curve presents a graphical view of the cumulative distribution of amenity resources and the Gini's Coefficient provides a single-parameter measure of the distributional concentration of amenity resources. Also the Gini's Coefficient is compared to the number of amenity resource for understanding distributional difference between concentration and quantitative distribution of amenity resources. The results demonstrate significantly different regional variation according to the amenity variables: almost intact nature, interaction between nature and man, man-made.

• Journal of Korean Society for Quality Management
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• v.29 no.3
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• pp.79-85
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• 2001

Estimation of the process deviation is an important problem in statistical process control, especially in the control chart, process capability analysis or measurement system analysis. In this paper we suggest the use of the Gini's mean difference for the estimation of the process deviation when we design the control limits in construction of the control charts. The efficiency of the Gini's mean difference was well explained in Nam, Lee and Jung(2000). In this paper we propose an $\overline{X}$ control chart which use the control limits based on the Gini's mean difference. In various classes of distributions, the proposed control chart shows food performance.

• Journal of Korea Water Resources Association
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• v.54 no.12
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• pp.1223-1232
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• 2021

In this study, a new analysis method by using a "Discharge Gini Coefficient" is presented to determine the degree of inequality in daily discharge throughout the year. The Discharge Gini Coefficient can be calculated using the area relationship with the cumulative percentage of the daily mode discharge in the ascending order according to the cumulative percentage of the date of occurrence of the daily discharge throughout the year. The Discharge Gini Coefficient is presented as a value between 0 and 1, and the degree of inequality can be divided into 5 levels. The Discharge Gini Coefficient can be used to estimate the discharge stability of the downstream point relative to the upstream point. In addition, it is possible to quantify the influence of each reference discharge on the total inequality. The applicability of the Discharge Gini Coefficient was reviewed using long-term daily discharge data at eight points upstream and downstream of the four major rivers in Korea. The Discharge Gini Coefficient can also be used to analyze the discharge control effect in the downstream by the upstream dam.