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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:

k123456789101112
Δhk50025010050251054321.51.25
$$j=h+\frac{\sum\limits_{k=1}^{12}{w_kX_k\left(h\times \Delta h_k\right)}}{\sum\limits_{k=1}^{12}{w_k} } ,$$

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)592616111110433211100000
Rank (i)123456789101112131415161718
h = 6

k123456789101112
Δhk50025010050251054321.51.25
h×Δhk3000150060030015060302418129.07.5
Count Cih×Δhk (Xk)000000122366
Weight (wk)1.000.500.330.250.200.170.140.120.110.100.090.08
wkXk0.000.000.000.000.000.000.140.250.220.300.550.50

The sum of wkXk = 1.9605 and the sum of wk = 3.1032, therefore j = 6 + 1.9605/3.1032 = 6.6318.

History

Yearj
19971.0000
19983.0884
19993.4311
20005.5061
20016.6318
20028.8126
200311.0112
200413.3679
200516.5813
200618.0604
200721.1944
200823.5425
200926.6016
201028.1149
201131.3627
201235.5044
201337.0119
201438.2202
201539.4949
201639.8552
201741.9382
201842.1928
201942.3590
202043.3805
202144.5787
202246.6402
202346.8427
202447.9501
202549.9040

References