# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## career years h-index by average citations per year

The career years h-index by average citations per year (Mahbuba and Rousseau 2013) is similar to the other two career years h-indices, but is based on the average number of citations generated per publication per year, rather than on the total publications or total citations for each year. One creates a list of years ranked by average citation count per publication 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 average citations per year is the largest value h for which at least h years have publications with an average of h citations.

$$\text{career years }h\text{ by average citations per year}=\underset{i}{\max}\left(i\leq \frac{C_i}{P_i}\right).$$

Because the average number of citations 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.

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

### Example

Years are ordered by average number of citations per publication from that year, from highest to lowest.

Year (yi) Publications (Pi) Citations (Ci) Average Citations per Publication(Ci/Pi) Rank (i) 1997 1998 2000 1999 2001 5 1 5 1 4 77 11 40 2 3 15.40 11.00 8.00 2.00 0.75 1 2 3 4 5 h = 3

The largest rank where i ≤ Ci/Pi is 3. The interpolated rank betweeen this and the next largest value is 3.89.

### History

YearCareer years hint by avg cites
19971.0000
19982.0000
19992.4000
20003.5000
20013.8889
20025.6250
20035.9091
20046.8462
20057.5000
20068.6667
200710.2500
200811.4000
200911.4762
201012.5909
201113.7647
201214.4211
201314.7200
201415.2941
201515.7241
201615.7500
201715.7500

## References

• Mahbuba, D., and R. Rousseau (2013) Year-based h-type indicators. Scientometrics 96(3):785–797.