# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## j-index (Todeschini)

The j-index (Todeschini 2011) is a modification of the h-index which allows for over-cited publications in the core to increase the overall value of the index. It uses a set of fixed categorical increases over h:

 k Δhk 1 2 3 4 5 6 7 8 9 10 11 12 500 250 100 50 25 10 5 4 3 2 1.5 1.25
$$j=h+\frac{\sum\limits_{k=1}^{12}{w_kX_k\left(h\times \Delta h_k\right)}}{\sum\limits_{k=1}^{12}{w_k} } ,$$

where $$w_k$$, the weight given to each category, is simply $$1/k$$, and $$X_k\left(h \times \Delta h_k\right)$$ is the count of publications whose citations are at least equal to $$h \times \Delta h_k$$.

Essentially this metric adds additional scores to h for publications which are cited well more than that necessary for the core, with larger weight given to those much higher than the core value (500 times the core get a weight of 1, 250 times the core get a weight of 0.5, etc.).

### Example

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

 Citations (Ci) Rank (i) 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 h = 6

 k Δhk h×Δhk Count Ci ≥ h×Δhk (Xk) Weight (wk) wkXk 1 2 3 4 5 6 7 8 9 10 11 12 500 250 100 50 25 10 5 4 3 2 1.5 1.25 3000 1500 600 300 150 60 30 24 18 12 9 7.5 0 0 0 0 0 0 2 2 2 3 6 6 1 0.5 0.33 0.25 0.2 0.17 0.14 0.12 0.11 0.1 0.09 0.08 0 0 0 0 0 0 0.29 0.25 0.22 0.3 0.55 0.5

The sum of wkXk = 2.1034 and the sum of wk = 3.1032, therefore j = 6 + 2.1034/3.1032 = 6.6778.

Yearj
19971.0000
19982.1803
19993.3257
20005.4112
20016.6778
20027.7935
20039.7703
200412.1640
200514.3768
200616.8052
200718.9074
200821.1863
200925.1645
201026.4376
201128.5540
201229.8242
201332.1643
201435.2275
201537.1586
201638.3459
201738.4342

## References

• Todeschini, R. (2011) The j-index: A new bibliometric index and multivariate comparisons between other common indices. Scientometrics 87:621–639.