# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## f-index (Tol)

If the h- and g-indices are the largest value x for which x publications have a minimum (h) or mean (g) number of citations equal to x, then Tol's f-index (Tol 2007) is the same idea, except based on the harmonic mean number of citations for the top f publications.

$$f=\underset{i}{\max}\left(\frac{1}{\frac{1}{i}\sum\limits_{j=1}^{i}{\frac{1}{C_j}}}\geq i\right)=\underset{i}{\max}\left(\frac{i}{\sum\limits_{j=1}^{i}{\frac{1}{C_j}} }\geq i\right)$$

### Example

Publications are ordered by number of citations, from highest to lowest.

 Citations (Ci) Rank (i) Harmonic Mean Citations 42 36 14 11 9 9 3 2 2 2 1 1 1 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 42.0 38.8 24.4 18.7 15.4 13.8 9.1 6.3 5.1 4.4 3.4 2.8 2.5 2.7 2.8 3.0 f = 7

The largest rank where i ≤ harmonic mean citations is 7.

Yearf
19971
19983
19994
20006
20017
20029
200312
200416
200518
200621
200724
200827
200930
201032
201135
201237
201338
201439
201540
201641
201742

## References

• Tol, R.S.J. (2007) Of the h-index and its alternatives: An application to the 100 most prolific economists (FNU-146). Sustainability and Global Change, Hamburg University.