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career years h-index by diffusion speed

The career years h-index by diffusion speed (Mahbuba and Rousseau 2013) is similar to the career years h-index by average citations per year, but rescales the citation counts per year for the time ellapsed since the year of publication. One could also calculate it for a fixed time window, but here we are using career length at the time of calcuation. One creates a list of years ranked by diffusion speed estimated for all citations for all publications from that year. This list is then processed in the same manner as a typical h-type index, namely the career years h-index by diffusion speed is the largest value h for which at least h years have a diffusion speed of h.

$$\text{career years }h\text{ by diffusion speed}=\underset{i}{\max}\left(i\leq \frac{C_i}{A_i}\right).$$

Because the diffusion speed will often not be an integer, the authors recommend interpolating between this and the next largest value, as with the real h-index, in order to more accurately estimate the metric.

$$h_{int}=\frac{\left(h+1\right)\frac{C_h}{A_h}-h\frac{C_{h+1}}{A_{h+1}}}{1-\frac{C_{h+1}}{A_{h+1}}+\frac{C_h}{A_h}}.$$

Example

Years are ordered by diffusion speed per year, from highest to lowest.

Year (yi)19972000199820011999
Age (Ai)52413
Citations (Ci)109171624
Diffusion Speed (Ci/Ai)21.808.504.002.001.33
Rank (i)12345
h = 3

The largest rank where i ≤ Ci/Ai is 3. The interpolated rank betweeen this and the next largest value is 3.33.

History

YearCareer years hint by diffusion speed
19971.0000
19982.0000
19992.2000
20003.2105
20013.3333
20024.9406
20035.4000
20045.8127
20056.5926
20066.7079
20077.3333
20088.4878
20098.6744
20109.6536
201110.5789
201210.6091
201310.6568
201411.3947
201511.6388
201611.6471
201711.5992
201811.5580
201911.7759
202012.2879
202112.2083
202212.1403
202312.7658
202412.7105
202512.8000

References