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) | 57 | 26 | 16 | 12 | 11 | 10 | 4 | 3 | 2 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| Harmonic Mean Citations | 57.0 | 35.7 | 25.3 | 19.8 | 17.1 | 15.3 | 10.9 | 8.2 | 6.1 | 4.0 | 3.2 | 2.7 | 2.4 | 2.6 | 2.7 | 2.9 | 3.1 | 3.3 |
| f = 8 |
The largest rank where i ≤ harmonic mean citations is 8.
History
| Year | f |
|---|---|
| 1997 | 1 |
| 1998 | 3 |
| 1999 | 4 |
| 2000 | 6 |
| 2001 | 8 |
| 2002 | 10 |
| 2003 | 13 |
| 2004 | 17 |
| 2005 | 20 |
| 2006 | 23 |
| 2007 | 27 |
| 2008 | 29 |
| 2009 | 31 |
| 2010 | 34 |
| 2011 | 37 |
| 2012 | 39 |
| 2013 | 41 |
| 2014 | 42 |
| 2015 | 43 |
| 2016 | 45 |
| 2017 | 46 |
| 2018 | 48 |
| 2019 | 50 |
| 2020 | 51 |
| 2021 | 53 |
| 2022 | 54 |
| 2023 | 55 |
| 2024 | 57 |
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.