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f-index (Tol)

If the h-index and g-index 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)472619151110432111100000
Rank (i)123456789101112131415161718
Harmonic Mean Citations47.033.526.722.318.516.211.38.46.24.13.22.72.42.62.82.93.13.3
f = 8

The largest rank where i ≤ harmonic mean citations is 8.

History

Yearf
19971
19983
19994
20006
20018
200211
200314
200417
200520
200623
200727
200829
200931
201034
201138
201239
201341
201442
201543
201645
201746
201848
201950
202051
202153
202254
202355
202455

References