## Gini coefficient |

In **Gini coefficient** (**Gini index**, or **Gini ratio**, is a *Variability and Mutability* (*Variabilità e mutabilità*).^{[1]}^{[2]}

The Gini coefficient measures the inequality among values of a ^{[3]}^{[4]} However, a value greater than one may occur if some persons represent negative contribution to the total (for example, having negative income or wealth). For larger groups, values close to or above 1 are very unlikely in practice. Given the normalization of both the cumulative population and the cumulative share of income used to calculate the Gini coefficient, the measure is not overly sensitive to the specifics of the income distribution, but rather only on how incomes vary relative to the other members of a population. The exception to this is in the redistribution of income resulting in a minimum income for all people. When the population is sorted, if their income distribution were to approximate a well-known function, then some representative values could be calculated.

The Gini coefficient was proposed by Gini as a measure of ^{[5]} For ^{[6]} African countries had the highest pre-tax Gini coefficients in 2008–2009, with South Africa the world's highest, variously estimated to be 0.63 to 0.7,^{[7]}^{[8]} although this figure drops to 0.52 after social assistance is taken into account, and drops again to 0.47 after taxation.^{[9]} The global income Gini coefficient in 2005 has been estimated to be between 0.61 and 0.68 by various sources.^{[10]}^{[11]}

There are some issues in interpreting a Gini coefficient. The same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population, or with a baby boom, experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient.^{[12]}^{[13]}^{[14]}

- definition
- calculation
- generalized inequality indices
- gini coefficients of income distributions
- gini coefficients of social development
- features of gini coefficient
- countries by gini index
- limitations of gini coefficient
- alternatives to gini coefficient
- relation to other statistical measures
- other uses
- see also
- references
- further reading
- external links

The Gini coefficient is a single number aimed at measuring the degree of inequality in a distribution. It is most often used in economics to measure how far a country's wealth or income distribution deviates from a totally equal distribution.

The Gini coefficient is usually defined *x* of the population (see diagram). The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the Lorenz curve (marked *A* in the diagram) over the total area under the line of equality (marked *A* and *B* in the diagram); i.e., G = *A*/(*A* + *B*). It is also equal to 2*A* and to 1 − 2*B* due to the fact that *A* + *B* = 0.5 (since the axes scale from 0 to 1).

If all people have non-negative income (or wealth, as the case may be), the Gini coefficient can theoretically range from 0 (complete equality) to 1 (complete inequality); it is sometimes expressed as a percentage ranging between 0 and 100. In practice, both extreme values are not quite reached. If negative values are possible (such as the negative wealth of people with debts), then the Gini coefficient could theoretically be more than 1. Normally the mean (or total) is assumed positive, which rules out a Gini coefficient less than zero.

An alternative approach is to define the Gini coefficient as half of the ^{[15]} The mean absolute difference is the average *x*_{i} is the wealth or income of person *i*, and there are *n* persons, then the Gini coefficient *G* is given by:

When the income (or wealth) distribution is given as a continuous *p*(*x*), the Gini coefficient is again half of the relative mean absolute difference:

where is the mean of the distribution, and the lower limits of integration may be replaced by zero when all incomes are positive.

Other Languages

Afrikaans: Gini-koëffisiënt

العربية: معامل جيني

asturianu: Coeficiente Gini

azərbaycanca: Cini indeksi

বাংলা: জিনি সহগ

беларуская: Каэфіцыент Джыні

беларуская (тарашкевіца): Каэфіцыент Джыні

भोजपुरी: गिनी गुणांक

български: Коефициент на Джини

català: Coeficient de Gini

čeština: Giniho koeficient

dansk: Gini-koefficient

Deutsch: Gini-Koeffizient

eesti: Gini koefitsient

Ελληνικά: Συντελεστής Τζίνι

español: Coeficiente de Gini

Esperanto: Koeficiento de Gini

euskara: Giniren koefiziente

فارسی: شاخص جینی

français: Coefficient de Gini

한국어: 지니 계수

հայերեն: Ջինիի գործակից

हिन्दी: गिनी गुणांक

hrvatski: Ginijev koeficijent

Igbo: Gini coefficient

Bahasa Indonesia: Koefisien Gini

italiano: Coefficiente di Gini

עברית: מדד ג'יני

ქართული: ჯინის კოეფიციენტი

kurdî: Qatjimara Giniyê

ລາວ: ສຳປະສິດຈິນີ

latviešu: Džini koeficients

lietuvių: Gini indeksas

magyar: Gini-index

मैथिली: गिनी गुणाङ्क

македонски: Џиниев коефициент

مازِرونی: جینی شاخص

Bahasa Melayu: Pekali Gini

Nederlands: Gini-coëfficiënt

नेपाली: गिनी गुणांक

日本語: ジニ係数

norsk: Gini-koeffisient

پښتو: شاخص جینی

ភាសាខ្មែរ: មេគុណជីនី

polski: Współczynnik Giniego

português: Coeficiente de Gini

română: Coeficientul lui Gini

русский: Коэффициент Джини

саха тыла: Дьини коэффициена

Scots: Gini coefficient

Simple English: Gini coefficient

slovenščina: Ginijev koeficient

српски / srpski: Џини коефицијент

srpskohrvatski / српскохрватски: Ginijev koeficijent

Basa Sunda: Koéfisién Gini

suomi: Gini-kerroin

svenska: Ginikoefficient

தமிழ்: ஜினி குறியீடு

татарча/tatarça: Джини коэффициенты

ไทย: สัมประสิทธิ์จีนี

Türkçe: Gini katsayısı

українська: Коефіцієнт Джині

اردو: جینی عددی سر

Tiếng Việt: Hệ số Gini

中文: 基尼系数