Concentration Index

From Open Risk Manual
(Redirected from Concentration Indicator)


A concentration index is any Mathematical Expression (function) that converts a distribution of observed values into a single number expressing the prevalence (Concentration) of certain observations amongst the total set. Concentration indexes are closely associated with inequality and diversity indexes


Concentration indexes find widespread use in (among others):

  • studies of biological diversity where the objective is to identify the representation of different species (number count of individuals) in a given ecological region
  • economic inequality, where the objective is to identify the distribution of income or other definitions of wealth amont participants in an economic system
  • market competition, where the objective is to identify the market share enjoyed by firms operating in a given market
  • different areas of Portfolio Management and Risk Management, where the objective is to identify and manage Concentration Risk

Table of Concentration and Diversity Indexes

The following table aims to be a complete enumeration of the essentially distinct varieties of concentration and diversity indexes:

Index Name Alternative Names Domain Remarks
Atkinson Index
Berger-Parker Index Special Case of the Concentration Ratio
Concentration Ratio
Generalized Entropy Index Theil Index, Renyi Index or Entropy Widely Used
Gini Index
Gini-Simpson Index Blau Index, Gibbs-Martin Index, Dominance 1 - Simpson Index
Hannah Kay Index
Hall-Tideman Index Rosenbluth Market Concentration Related to the Gini Index
Hoover Index
Herfindahl-Hirschman Index Hefindahl Index Widely Used in Finance 1 - Simpson
Inverse Simpson Index Inverse of the Simpon Index (Hence of the HHI)
Kolm Index
Menhinick Index
Margalef Index
Richness Index Species Richness Biodiversity Simply the number of categories / taxa
Simpson Index Widely Used in Biodiversity 1 - HHI
Shannon Index Shannon-Weaver, Shannon-Wiener Index or Entropy Widely Used Special case of the Generalized Entropy Index

Spatial and Geographic Concentration Indexes

When spatial distribution (e.g., geographic location) is an important consideration the above general indexes may have reduced applicability. In this case a specialized type of Geographic Concentration Index might more applicable. Several geographic concentration indexes have been proposed:

  • Generalization of the Gini index
  • Generalization of the Herfindahl index
  • Multigroup Thiel index
  • Ellison and Glaeser index
  • Maurel and Sedillot index
  • Continuous indexes that use distances between locations

Issues and Challenges

  • The very widespread use of concentration indexes means that the same essential functions have been invented many times separately, have been given different names and are used in slightly different manner (inverse relationships, with different normalizations etc.).
  • The reduction of Concentration Measurement to a single number is only one of the available quantitative tools to support an analysis. The Lorentz Curve is an example of a more complex approach to studying concentration.

See Also