方法对比

	Lorenz Curve	Atkinson Index	Palma Ratio
领域	Sociology	Sociology	Sociology
方法族	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1905	1970	2011 (Palma's finding); 2013–2014 (the ratio)
提出者	Max Otto Lorenz	Anthony Barnes Atkinson	Gabriel Palma; named by Cobham & Sumner
类型	Graphical representation of distributional inequality	Welfare-based, parameterized inequality index	Tail-ratio inequality measure
开创性文献	Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70), 209–219.	Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244–263.	Cobham, A., & Sumner, A. (2014). Is inequality all about the tails? The Palma measure of income inequality. Significance, 11(1), 10–13.
别名	Lorenz concentration curve, Lorenz diagram, cumulative share curve	Atkinson inequality measure, Atkinson's A, welfare-based inequality index	Palma index, Palma measure, top10/bottom40 ratio
相关	5	5	5
摘要	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 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 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.