方法对比

	Gini Coefficient	Atkinson Index	Lorenz Curve	Palma Ratio
领域	Sociology	Sociology	Sociology	Sociology
方法族	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1912	1970	1905	2011 (Palma's finding); 2013–2014 (the ratio)
提出者	Corrado Gini	Anthony Barnes Atkinson	Max Otto Lorenz	Gabriel Palma; named by Cobham & Sumner
类型	Scalar measure of statistical dispersion / inequality	Welfare-based, parameterized inequality index	Graphical representation of distributional inequality	Tail-ratio inequality measure
开创性文献	Ceriani, L., & Verme, P. (2012). The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini. The Journal of Economic Inequality, 10(3), 421–443.	Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244–263.	Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70), 209–219.	Cobham, A., & Sumner, A. (2014). Is inequality all about the tails? The Palma measure of income inequality. Significance, 11(1), 10–13.
别名	Gini index, Gini ratio, Gini concentration ratio, G	Atkinson inequality measure, Atkinson's A, welfare-based inequality index	Lorenz concentration curve, Lorenz diagram, cumulative share curve	Palma index, Palma measure, top10/bottom40 ratio
相关	5	5	5	5
摘要	The Gini coefficient is the most widely used single-number summary of inequality in a distribution such as income or wealth. Introduced by the Italian statistician Corrado Gini in 1912, it equals twice the area between the Lorenz curve and the line of perfect equality, ranging from 0 when everyone has the same amount to a maximum approaching 1 when one unit holds everything.	The Atkinson index is a welfare-based measure of inequality that incorporates an explicit, analyst-chosen parameter for how much society dislikes inequality. Introduced by Anthony Atkinson in 1970, it asks what fraction of total income could be discarded, under an equal distribution, while leaving social welfare unchanged — making the ethical judgement behind any inequality comparison transparent rather than hidden.	The Lorenz curve is a graphical device that displays the full shape of inequality in a distribution by plotting the cumulative share of a quantity (such as income) held by the cumulative share of the population, ranked from poorest to richest. Introduced by Max Lorenz in 1905, it underlies the Gini coefficient and provides the basis for ranking distributions by inequality when one curve lies entirely above another.	The Palma ratio measures income inequality as the ratio of the income share held by the richest 10 percent of the population to the share held by the poorest 40 percent. It rests on the empirical regularity, documented by Gabriel Palma, that the middle deciles (5 through 9) capture a remarkably stable half of national income across countries, so that inequality is essentially a contest between the top and the bottom — the 'tails' of the distribution.