The repeat rate: from Hirschman to Stirling
In this short note we recall the history and definition of the repeat rate, also known as the Hirschman–Herfindahl index or as the Simpson index, and show that its generalization to a measure that includes disparity between items, known as the Rao-Stirling index, or a monotone transformation of it, is an acceptable diversity measure which, however, does not meet the ‘monotonicity of balance’ requirement.
KeywordsRepeat rate Hirschman index Simpson index Herfindahl index Rao-Stirling index Measuring diversity Interdisciplinarity
We thank Loet Leydesdorff for helpful observations about an earlier version of this note.
- Good, I. J. (1982). Comment [on Patil & Taillie, 1982]. Journal of the American Statistical Association, 77(379), 561–563.Google Scholar
- Herfindahl, O. C. (1950). Concentration in the U.S. steel industry. Doctoral dissertation, Columbia University.Google Scholar
- Hirschman, A. O. (1945). National power and the structure of foreign trade. Berkeley: University of California Press.Google Scholar
- Hirschman, A. O. (1964). The paternity of an index. The American Economic Review, 54(5), 761–762.Google Scholar
- Mugabushaka, A.-M., Kyriakou, A., & Papazoglou, T. (2015). Bibliometric indicators of interdisciplinarity exploring new class of diversity measures. In A. A. Salah, Y. Tonta, A. A. A. Salah, C. Sugimoto, & U. Al (Eds.), Proceedings of ISSI 2015 (pp. 397–402). Istanbul: Boğaziçi University Printhouse.Google Scholar
- Nijssen, D., Rousseau, R., & Van Hecke, P. (1998). The Lorenz curve: A graphical representation of evenness. Coenoses, 13(1), 33–38.Google Scholar
- Rousseau, R., Hu, X. J., & Zhang, L. (2018). Knowledge integration: Its meaning and measurement. In: W. Glänzel, H. Moed, U. Schmoch, & M. Thelwall (Eds.), Springer Handbook of Science and Technology Indicators. (To appear).Google Scholar