手法を比較

	Lorenz Curve	Index of Dissimilarity	Palma Ratio
分野	Sociology	Sociology	Sociology
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1905	1955	2011 (Palma's finding); 2013–2014 (the ratio)
提唱者	Max Otto Lorenz	Otis Dudley Duncan & Beverly Duncan	Gabriel Palma; named by Cobham & Sumner
種類	Graphical representation of distributional inequality	Index of evenness of two groups across units	Tail-ratio inequality measure
原典	Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70), 209–219.	Duncan, O. D., & Duncan, B. (1955). A methodological analysis of segregation indexes. American Sociological Review, 20(2), 210–217.	Cobham, A., & Sumner, A. (2014). Is inequality all about the tails? The Palma measure of income inequality. Significance, 11(1), 10–13.
別名	Lorenz concentration curve, Lorenz diagram, cumulative share curve	dissimilarity index, Duncan index, D index, segregation index	Palma index, Palma measure, top10/bottom40 ratio
関連	5	5	5
概要	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 index of dissimilarity, often called the Duncan segregation index, measures how unevenly two groups — such as two racial or occupational groups — are distributed across a set of units like neighborhoods, schools, or occupations. It ranges from 0, when both groups have identical distributions across units, to 1, when the units are completely segregated, and has the intuitive interpretation of the share of one group that would have to relocate to achieve an even distribution.	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.