Evolutionary Biological Data Science Laboratory

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

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

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)	57	26	16	12	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
						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	4	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	0.40	0.55	0.50

The sum of w_kX_k = 2.0605 and the sum of w_k = 3.1032, therefore j = 6 + 2.0605/3.1032 = 6.6640.

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