# Rosenbluth index

The **Rosenbluth Index** (also **Rosenbluth concentration coefficient** ) is an index for the absolute concentration on markets. It is a statistical measure of concentration .

It is used to measure the concentration (or unequal distribution) of *n * market participants , who each have a market share *h _{i}* and a rank

*i*(ordered according to decreasing market shares) . The Rosenbluth index is based on a graphic representation of the market shares: the market participants are entered on the X-axis (sorted in decreasing order of size), the market shares for the first, the first two, the first three (etc. .) Market participants. The result is a curve of market shares from zero to 1 (100 percent).

The Rosenbluth Index is defined as:

Here, *h _{i is}* the frequency of the respective expression;

*i*the rank of the feature bearer;

*A*is the area above the concentration curve; since it is 0.5 for a single market participant (monopoly, 100%) - the curve halves the square from (0 | 0) to (1 | 1) - the area is multiplied by 2; at a maximum concentration (monopoly, complete inequality) the Rosenbluth index is therefore 1. At a minimum concentration (egalitarian distribution) the Rosenbluth index is 1 /

*n*.

## literature

- Rosenbluth, G. (1955):
*Measures of Concentration*. In: GJ Stigler (ed.):*Business Concentration and Price Policy by National Bureau of Economic Research*. Princeton: Princeton University Press - Rosenbluth, G. (1957):
*Concentration in Canadian Manufacturing Industries*. Princeton: Princeton University Press