Measuring Concentration in Data with an Exogenous Order

Abedieh, Jasmin; Groll, Andreas and Eugster, Manuel J. A. (8. February 2013): Measuring Concentration in Data with an Exogenous Order. Department of Statistics: Technical Reports, No.140

Abstract

Concentration measures order the statistical units under observation according to their market share. However, there are situations where an order according to an exogenous variable is more appropriate or even required. The present article introduces a generalized definition of market concentration and defines a corresponding concentration measure. It is shown that this generalized concept of market concentration satisfies the common axioms of (classical) concentration measures. In an application example, the proposed approach is compared with classical concentration measures; the data are transfer spendings of German Bundesliga soccer teams, the ``obvious'' exogenous order of the teams is the league ranking.

• Item Type: Paper
• Keywords: Market concentration, Concentration measure, Exogenous order, German Bundesliga
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Technical Reports; Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• Language: English