Evolutionary Biological Data Science Laboratory

rational h-index

The rational h-index (Ruane and Tol 2008) (h^Δ or h_rat) is a continuous version of the h-index which not only measures the standard h-index but includes the fractional progress toward the next higher value of h. It is calculated as

$$h^\Delta = h + 1 -\frac{n}{2h+1},$$where \(n\) is the number of citations necessary to reach the next value of \(h\). The divisor, \(2h+1\), is the maximum number of possible citations needed to move from \(h\) to \(h+1\) (one additional citation for each of the \(h\) publications in the core plus \(h+1\) citations for a publication outside of the core with no citations). Practically speaking, \(n\) is the number of publications in the core with exactly \(h\) citations (thus needing one more to allow a move to \(h+1\)) plus \(h+1-C_{h+1}\) (the number of citations the \(h+1\)^th ranked publication needs to reach \(h+1\) citations).

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

The h-index is 6. To reach an h of 7, we would need to add 0 citations to the publications within the core and 3 citations to the 7^th publication (for a total of 3). The maximum number of citations that could be required is 13 (if all 6 core publications had exactly 6 citations and the 7^th publication had zero), thus the rational h is 6 + 1 - 3/13 = 6.7692.

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