Compare methods

	Isolation Index	Atkinson Index	Lorenz Curve
Field	Sociology	Sociology	Sociology
Family	Process / pipeline	Process / pipeline	Process / pipeline
Year of origin	1954	1970	1905
Originator	Wendell Bell (formalization of P* indices)	Anthony Barnes Atkinson	Max Otto Lorenz
Type	Exposure-dimension segregation index	Welfare-based, parameterized inequality index	Graphical representation of distributional inequality
Seminal source	Bell, W. (1954). A probability model for the measurement of ecological segregation. Social Forces, 32(4), 357–364.	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.
Aliases	P* isolation index, interaction index, exposure index, Bell isolation index	Atkinson inequality measure, Atkinson's A, welfare-based inequality index	Lorenz concentration curve, Lorenz diagram, cumulative share curve
Related	5	5	5
Summary	The isolation index measures the exposure dimension of segregation: the extent to which members of a minority group are exposed only to one another rather than to members of other groups. It answers the question 'what is the own-group share of the typical neighbor (or classmate, or coworker) that a member of the focal group encounters?' Unlike evenness measures, it depends on the relative size of the group as well as its spatial distribution.	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.