Lorenzkäyrään

Lorenzkäyrän, commonly referred to as the Lorenz curve in statistics, is a graphical representation of the distribution of a variable across a population, most often income or wealth. The horizontal axis shows the cumulative share of individuals, arranged from the poorest to the richest, while the vertical axis shows the corresponding cumulative share of the variable. A diagonal line from (0,0) to (1,1) represents perfect equality; the actual curve typically lies below this line when inequality exists.

Origin and use: Named after Max O. Lorenz, who introduced the concept in 1905. The Lorenz curve has become a standard tool in economics and statistics for visualizing inequality and for comparing distributions across groups or over time. It is often used in conjunction with summary measures such as the Gini coefficient.

Calculation and interpretation: Data are sorted by the variable of interest, and cumulative shares p (population) and L(p) (the variable) are plotted to form the curve. The area between the line of equality and the Lorenz curve is related to the Gini coefficient, a widely used scalar of inequality. A curve close to the diagonal indicates low inequality, while a curve far from the diagonal indicates higher inequality.

Limitations: The Lorenz curve reduces a distribution to a single shape and does not capture all aspects of distribution, such as tail behavior or multidimensional inequality. It can also be sensitive to the population unit and to the data’s grouping or aggregation.

See also: Gini coefficient, Palma ratio, Theil index.