Shannon's diversity index (Diversity metric)

## Details

$$SHDI = - \sum \limits_{i = 1}^{m} (P_{i} * \ln P_{i})$$ where \(P_{i}\) is the proportion of class i.

SHDI is a 'Diversity metric'. It is a widely used metric in biodiversity and ecology and takes both the number of classes and the abundance of each class into account.

## References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Shannon, C., and W. Weaver. 1949. The mathematical theory of communication. Univ. IllinoisPress, Urbana