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The Gini coefficient (also known as the Gini index or Gini ratio) ( ) is a measure of statistical dispersion intended to represent the income distribution of a nation's residents, and is the most commonly used measure of inequality. It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper "Variability and Mutability" ((イタリア語:Variabilità e mutabilità)).〔Gini, C. (1912). "''(イタリア語:Variabilità e mutabilità)''" 'Variability and Mutability', C. Cuppini, Bologna, 156 pages. Reprinted in ''Memorie di metodologica statistica'' (Ed. Pizetti E, Salvemini, T). Rome: Libreria Eredi Virgilio Veschi (1955).〕〔Gini, C. (1909). "Concentration and dependency ratios" (in Italian). English translation in ''Rivista di Politica Economica'', 87 (1997), 769–789.〕 The Gini coefficient measures the inequality among values of a frequency distribution (for example, levels of income). A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income). A Gini coefficient of one (or 100%) expresses maximal inequality among values (for example, where only one person has all the income or consumption, and all others have none).〔(【引用サイトリンク】url=http://www.census.gov/population/www/cps/cpsdef.html )〕〔Note: Gini coefficient becomes 1, only in a large population where one person has all the income. In the special case of just two people, where one has no income and the other has all the income, the Gini coefficient is 0.5. For 5 people set, where 4 have no income and the fifth has all the income, the Gini coefficient is 0.8. See: (FAO, United Nations – Inequality Analysis, The Gini Index Module ) (PDF format), fao.org.〕 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. The Gini coefficient was proposed by Gini as a measure of inequality of income or wealth.〔Gini, C. (1936). "On the Measure of Concentration with Special Reference to Income and Statistics", Colorado College Publication, General Series No. 208, 73–79.〕 For OECD countries, in the late 2000s, considering the effect of taxes and transfer payments, the income Gini coefficient ranged between 0.24 to 0.49, with Slovenia the lowest and Chile the highest. 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,〔(【引用サイトリンク】publisher=KPMG )〕〔(【引用サイトリンク】publisher=United Nations Development Program )〕 although this figure drops to 0.52 after social assistance is taken into account, and drops again to 0.47 after taxation. The global income Gini coefficient in 2005 has been estimated to be between 0.61 and 0.68 by various sources.〔 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.〔 ==Definition== 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 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., . 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 would be to consider the Gini coefficient as half of the relative mean absolute difference, which is a mathematical equivalence . The mean absolute difference is the average absolute difference of all pairs of items of the population, and the relative mean absolute difference is the mean absolute difference divided by the average, to normalize for scale. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gini coefficient」の詳細全文を読む スポンサード リンク
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