Konzentrationsmaße

Konzentrationsmaße are statistical measures used to quantify the degree of concentration or inequality in a distribution. They are frequently applied in economics to assess income or wealth distribution, but can also be used in other fields to analyze market structures, resource allocation, or spatial patterns. The fundamental idea behind these measures is to compare the actual distribution of a variable to a hypothetical state of perfect equality, where each unit receives an equal share. A higher value of a Konzentrationsmaß typically indicates a more unequal or concentrated distribution, while a value closer to zero signifies a more even distribution.

Several different Konzentrationsmaße exist, each with its own mathematical formulation and properties. Some of the most common include the Gini coefficient, the Herfindahl-Hirschman Index (HHI), and the Lorenz curve. The Gini coefficient, derived from the Lorenz curve, ranges from 0 (perfect equality) to 1 (perfect inequality). The HHI is widely used in antitrust analysis to measure market concentration, calculated as the sum of the squares of the market shares of all firms in a market. The Lorenz curve itself is a graphical representation that plots the cumulative percentage of total income or wealth against the cumulative percentage of the population, with the line of perfect equality serving as a benchmark. The choice of which Konzentrationsmaß to use depends on the specific context and the nature of the data being analyzed.