# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## citation distribution score index

The citation distribution score index (Vinkler 2011, 2013) is a weighted sum of publication counts in a set of pre-defined citation-count-based categories. The 14 categories are defined predominantly by their upper limits, with the kth category usually having an upper limits of 2k citations, except for the first category which has an upper limit of 20 = 1 citation, and the last category, which has no upper limit.

CategoryRange of
Citations
Minimum
Citations
Maximum
Citations
10–2001
2(20+1)–2224
3(22+1)–2358
4(23+1)–24916
5(24+1)–251732
6(25+1)–263364
7(26+1)–2765128
8(27+1)–28129256
9(28+1)–29257512
10(29+1)–2105131024
11(210+1)–21110252048
12(211+1)–21220494096
13(212+1)–21340978192
14(212+1)–∞>8192

The rank of each category is also its weight. If Pk is the count of publications within the kth category, then the index is calculated as

$$\text{CDS}=\sum\limits_{k=1}^{14}{k P^k}.$$

### Example

Publications are ordered by number of citations, from highest to lowest.

 Citations (Ci) 42 36 14 11 9 9 3 2 2 2 1 1 1 0 0 0

Category
(k)
Citation
Range
Count of Pubs
in Range
(Pk)
kPk
10–166
22–448
35–800
49–16416
517–3200
633–64212

The index is the sum of kPk, thus CDS = 42.

YearCDS
19975
199810
199916
200029
200142
200258
200377
200498
2005120
2006144
2007158
2008180
2009196
2010222
2011243
2012257
2013275
2014292
2015310
2016320
2017328

## References

• Vinkler, P. (2011) Application of the distribution of citations among publications in scientometric evaluations. Journal of the American Society for Information Science and Technology 62(10):1963–1978.
• Vinkler, P. (2013) Would it be possible to increase the Hirsch-index, π-index or CDS-index by increasing the number of publications or citations only by unity? Journal of Informetrics 7(1):72–83.