| Lorenz Curve |
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| CATEGORIES ABOUT LORENZ CURVE | |
| economics curves | |
| welfare economics | |
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EXPLANATION Every point on the Lorenz curve represents a statement like "the bottom 20% of all households have 10% of the total income". A perfectly equal income distribution would be one in which every person has the same income. In this case, the bottom ''N''% of society would always have ''N''% of the income. This can be depicted by the straight line ''y'' = ''x''; called the line of perfect equality or the 45° line. By contrast, a perfectly unequal distribution would be one in which one person has all the income and everyone else has none. In that case, the curve would be at ''y'' = 0 for all ''x'' < 100, and ''y'' = 100 when ''x'' = 100. This curve is called the line of perfect inequality. If the variable being measured cannot take negative values, it is impossible for the Lorenz curve to rise above the line of perfect equality, or sink below the line of perfect inequality; it is increasing and Convex to the ''y''-axis. The Gini Coefficient is the area between the line of perfect equality and the observed Lorenz curve, as a percentage of the area between the line of perfect equality and the line of perfect inequality. For any distribution, the Lorenz curve ''L''(''F'') is written in terms of the Probability Density Function (''f''(''x'')) or the cumulative distribution function (''F''(''x'')) as: : where ''x''(''F'') is the inverse of the cumulative distribution function ''F''(''x'') (for example, see the Pareto Distribution ). REFERENCES Lorenz, M. O. (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association. 9: 209-219. Will Dawson's contributions'' SEE ALSO
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