# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## t-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 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) Rank (i) Geometric 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 38.9 27.7 22.0 18.4 16.3 12.8 10.2 8.5 7.3 6.1 5.3 4.6 4.2 3.8 3.5 t = 8

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

Yeart
19971
19983
19994
20007
20018
200211
200314
200418
200521
200624
200728
200831
200933
201036
201139
201241
201344
201445
201547
201648
201749

## 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.