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 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Δhk | 500 | 250 | 100 | 50 | 25 | 10 | 5 | 4 | 3 | 2 | 1.5 | 1.25 |
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) | 59 | 26 | 16 | 11 | 11 | 10 | 4 | 3 | 3 | 2 | 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 |
h = 6 |
k | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Δhk | 500 | 250 | 100 | 50 | 25 | 10 | 5 | 4 | 3 | 2 | 1.5 | 1.25 |
h×Δhk | 3000 | 1500 | 600 | 300 | 150 | 60 | 30 | 24 | 18 | 12 | 9.0 | 7.5 |
Count Ci ≥ h×Δhk (Xk) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | 2 | 3 | 6 | 6 |
Weight (wk) | 1.00 | 0.50 | 0.33 | 0.25 | 0.20 | 0.17 | 0.14 | 0.12 | 0.11 | 0.10 | 0.09 | 0.08 |
wkXk | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.25 | 0.22 | 0.30 | 0.55 | 0.50 |
The sum of wkXk = 1.9605 and the sum of wk = 3.1032, therefore j = 6 + 1.9605/3.1032 = 6.6318.
History
Year | j |
---|---|
1997 | 1.0000 |
1998 | 3.0884 |
1999 | 3.4311 |
2000 | 5.5061 |
2001 | 6.6318 |
2002 | 8.8126 |
2003 | 11.0112 |
2004 | 13.3679 |
2005 | 16.5813 |
2006 | 18.0604 |
2007 | 21.1944 |
2008 | 23.5425 |
2009 | 26.6016 |
2010 | 28.1149 |
2011 | 31.3627 |
2012 | 35.5044 |
2013 | 37.0119 |
2014 | 38.2202 |
2015 | 39.4949 |
2016 | 39.8552 |
2017 | 41.9382 |
2018 | 42.1928 |
2019 | 42.3590 |
2020 | 43.3805 |
2021 | 44.5787 |
2022 | 46.6402 |
2023 | 46.8427 |
2024 | 47.9501 |
2025 | 49.9040 |
References
- Todeschini, R. (2011) The j-index: A new bibliometric index and multivariate comparisons between other common indices. Scientometrics 87:621–639.