Concentration Index versus Diversity Index

Concentration Index versus Diversity Index

Concentration indexes and diversity indexes are related families of metrics that aim to assess the prevalence of some category within a broader set.

Discrete versus Continuous data sets

The main different between a concentration index and a diversity index is in the nature of the statistical observations that are used as input data for the index calculation. There are two possible starting points for input data:

• The population attributes used as observations are discrete (See Categorical Variable)
• Observations are numerical (See Numerical Variable), typically continuous and summable

Examples

• Discrete: For example $p_{i}={\frac {n_{i}}{N}}$ is the proportion of individuals in a population with total count N that belongs to Category i. A number of indexes used in diversity studies (Abundance, Richness, Margalev's, Menhinick’s diversity indexes) are based on such species counts.
• Numerical For example $E_{i}$ is a range of observations of some continuous quantity E such as risk Exposure or income. Such data will typically converted into weights $w_{i}={\frac {E_{i}}{E_{T}}}$