Simpson index

This is also the formula for the inverse Simpson index, or the true diversity of order 2.

This form of the Simpson index is also known as the Hunter-Gaston index in microbiology.

The inverse Simpson index equals:

Often researchers use the values given by one or more diversity indices, such as species richness, the Shannon index or the Simpson index.

The original Simpson index λ equals the probability that two entities taken at random from the dataset of interest (with replacement) represent the same type.

The Simpson index was introduced in 1949 by Edward H. Simpson to measure the degree of concentration when individuals are classified into types.

Both of these have also been called the Simpson index in the ecological literature, so care is needed to avoid accidentally comparing the different indices as if they were the same.

Simpson index is sometimes transformed by subtracting the observed value from the maximum possible value of 1, and then it is known as Gini-Simpson Index.

With a black and minority ethnic population of 3% in 2001, Cranham and Upminster wards have the lowest Simpson index for ethnic diversity in London.

The most popular of such indices have been the inverse Simpson index (1/λ) and the Gini-Simpson index (1 - λ).

As a result, the same measure is usually known as the Simpson index in ecology, and as the Herfindahl index or the Herfindahl-Hirschman index (HHI) in economics.

Such indices include species richness, the Shannon index, the Simpson index and the complement of the Simpson index (also known as the Gini-Simpson index).

Simpson index scales as mirror opposite to Gini; that is, with increasing diversity Simpson index takes a smaller value (0 means maximum, 1 means minimum heterogeneity per classic Simpson index).