t-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 t-index (Tol 2007) is the same idea, except based on the geometric mean number of citations for the top t publications.
$$t=\underset{i}{\max}\left(\exp\left(\frac{1}{i}\sum\limits_{j=1}^{i}\ln{C_j}\right)\geq i\right)$$Example
Publications are ordered by number of citations, from highest to lowest.
| Citations (Ci) | 47 | 26 | 19 | 15 | 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 |
| Geometric Mean Citations | 47.0 | 35.0 | 28.5 | 24.3 | 20.7 | 18.4 | 14.8 | 12.1 | 9.9 | 7.9 | 6.5 | 5.6 | 4.9 | 4.4 | 4.0 | 3.6 | 3.4 | 3.1 |
| t = 9 |
The largest rank where i ≤ geometic mean citations is 9.
History
| Year | t |
|---|---|
| 1997 | 1 |
| 1998 | 3 |
| 1999 | 5 |
| 2000 | 7 |
| 2001 | 9 |
| 2002 | 12 |
| 2003 | 16 |
| 2004 | 20 |
| 2005 | 23 |
| 2006 | 27 |
| 2007 | 30 |
| 2008 | 33 |
| 2009 | 35 |
| 2010 | 40 |
| 2011 | 43 |
| 2012 | 45 |
| 2013 | 48 |
| 2014 | 49 |
| 2015 | 52 |
| 2016 | 54 |
| 2017 | 55 |
| 2018 | 57 |
| 2019 | 59 |
| 2020 | 61 |
| 2021 | 63 |
| 2022 | 64 |
| 2023 | 66 |
| 2024 | 66 |
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.