# Gini coefficient

**Gini indexGini ratioGiniequalityGini coefficientsconcentration of wealthGini frameworkGini measure of inequalityGini valuesinequality**

In economics, the Gini coefficient, sometimes called Gini index, or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality.wikipedia

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### Economic inequality

**income inequalityinequalitywealth gap**

In economics, the Gini coefficient, sometimes called Gini index, or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality.

There are many methods for measuring economic inequality, with the Gini coefficient being a widely used one.

### Distribution of wealth

**wealth inequalitywealth distributionWealth condensation**

In economics, the Gini coefficient, sometimes called Gini index, or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality.

In fact it is a comparison to a diagonal society that is the basis for the Gini values used as a measure of the disequity in a particular economy.

### Corrado Gini

**GiniGini, Corrado**

It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability (Variabilità e mutabilità).

Corrado Gini (Motta di Livenza, 23 May 1884 – Rome, 13 March 1965) was an Italian statistician, demographer and sociologist who developed the Gini coefficient, a measure of the income inequality in a society.

### Income distribution

**distribution of incomeincomedistribution**

In economics, the Gini coefficient, sometimes called Gini index, or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality.

The Lorenz curve is closely associated with measures of income inequality, such as the Gini coefficient.

### Income inequality metrics

**income inequalitywage inequalitydispersion of incomes**

The Gini coefficient was proposed by Gini as a measure of inequality of income or wealth.

Among the most common metrics used to measure inequality are the Gini index (also known as Gini coefficient), the Theil index, and the Hoover index.

### Mean absolute difference

**MDMean differenceRelative mean absolute difference**

An alternative approach is to define the Gini coefficient as half of the relative mean absolute difference, which is mathematically equivalent to the Lorenz curve definition.

A related statistic is the relative mean absolute difference, which is the mean absolute difference divided by the arithmetic mean, and equal to twice the Gini coefficient.

### Pareto principle

**80/20 rule80-20 rule80:20 Rule**

The proverbial case where the richest 20% have 80% of all income (see Pareto principle) would lead to an income Gini coefficient of at least 60%.

Still, the Gini index of the world shows that nations have starkly varying wealth distributions.

### Redistribution of income and wealth

**redistribution of wealthincome redistributionwealth redistribution**

The exception to this is in the redistribution of income resulting in a minimum income for all people.

The difference between the Gini index for the income distribution before taxation and the Gini index after taxation is an indicator for the effects of such taxation.

### Statistical dispersion

**dispersionvariabilityspread**

### Social inequality

**inequalitysocial inequalitiesracial inequality**

The Gini coefficient was proposed by Gini as a measure of inequality of income or wealth.

A better measure at that level, however, is the Gini coefficient, a measure of statistical dispersion used to represent the distribution of a specific quantity, such as income or wealth, at a global level, among a nation's residents, or even within a metropolitan area.

### Lorenz curve

**incomeLorenz**

The Gini coefficient is usually defined mathematically based on the Lorenz curve, which plots the proportion of the total income of the population (y axis) that is cumulatively earned by the bottom x of the population (see diagram).

The Gini coefficient is the ratio of the area between the line of perfect equality and the observed Lorenz curve to the area between the line of perfect equality and the line of perfect inequality.

### Income

**incomesearningsearning power**

The Gini coefficient measures the inequality among values of a frequency distribution (for example, levels of income).

It can be measured by various methods, including the Lorenz curve and the Gini coefficient.

### Beta distribution

**beta betabeta of the first kind**

The Gini coefficient for the Beta distribution is half of the relative mean absolute difference:

### Progressive tax

**progressiveprogressive taxationprogressive income tax**

Developing countries like Brazil have also improved basic services like health care, education, and sanitation; others like Chile and Mexico have enacted more progressive tax policies.

Indices such as the Suits index, Gini coefficient, Kakwani index, Theil index, Atkinson index, and Hoover index have been created to measure the progressivity of taxation, using measures derived from income distribution and wealth distribution.

### Globalization

**globalisationglobalizedglobal**

This is attributed to globalization increasing incomes for billions of poor people, mostly in India and China.

They challenge directly traditional metrics, such as GDP, and look to other measures, such as the Gini coefficient or the Happy Planet Index, and point to a "multitude of interconnected fatal consequences–social disintegration, a breakdown of democracy, more rapid and extensive deterioration of the environment, the spread of new diseases, increasing poverty and alienation" which they claim are the unintended consequences of globalization.

### Anthony Shorrocks

**Anthony F. ShorrocksShorrocks index**

In 1978, Anthony Shorrocks introduced a measure based on income Gini coefficients to estimate income mobility.

In 1978, he introduced a measure based on income Gini coefficients to estimate income mobility.

### Atkinson index

For example, entropy measures are frequently used (e.g. the Atkinson index or the Theil Index and Mean log deviation as special cases of the generalized entropy index).

### Generalized entropy index

For example, entropy measures are frequently used (e.g. the Atkinson index or the Theil Index and Mean log deviation as special cases of the generalized entropy index).

Many popular indices, including Gini index, do not satisfy additive decomposability.

### Receiver operating characteristic

**ROC curveAUCROC**

The Gini coefficient is sometimes alternatively defined as twice the area between the receiver operating characteristic (ROC) curve and its diagonal, in which case the AUC (Area Under the ROC Curve) measure of performance is given by.

The AUC is related to the Gini coefficient (G_1) by the formula, where:

### Theil index

For example, entropy measures are frequently used (e.g. the Atkinson index or the Theil Index and Mean log deviation as special cases of the generalized entropy index).

The decomposability is a property of the Theil index which the more popular Gini coefficient does not offer.

### Economics

**economiceconomisteconomic theory**

### Statistics

**statisticalstatistical analysisstatistician**

It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability (Variabilità e mutabilità).

### Sociology

**sociologistsociologicalsociologists**

It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability (Variabilità e mutabilità).

### Frequency distribution

**distributionfrequency tabledistributions**

The Gini coefficient measures the inequality among values of a frequency distribution (for example, levels of income).

### Wealth

**Savingsaffluentwealthy**

However, a value greater than one may occur if some persons represent negative contribution to the total (for example, having negative income or wealth).