Basic properties that a suitable measure of income inequality should possess

The concept of inequality is distinct from that of poverty and fairness. Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income, and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general.

While different theories may try to explain how income inequality comes about, income inequality metrics simply provide a system of measurement used to determine the dispersion of incomes.

In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values.

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It is often used to represent income distribution, where it shows for the bottom x% of households, what percentage y% of the total income they have. The percentage of households is plotted on the x-axis, the percentage of income on the y-axis.

It can also be used to show distribution of assets. In such use, many economists consider it to be a measure of social inequality. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution.

The concept is useful in describing inequality among the size of individuals in ecology and in studies of biodiversity, where cumulative proportion of species is plotted against cumulative proportion of individuals.

The Lorenz curve is not defined if the mean of the probability distribution is zero or infinite.

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The Lorenz curve for a probability distribution is a continuous function. However, Lorenz curves representing discontinuous functions can be constructed as the limit of Lorenz curves of probability distributions, the line of perfect inequality being an example.

The information in a Lorenz curve may be summarised by the Gini coefficient and the Lorenz asymmetry coefficient.

If the variable being measured cannot take negative values, the Lorenz curve: cannot rise above the line of perfect equality, cannot sink below the line of perfect inequality, is increasing, and convex.