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.
| Category | Range of Citations | Minimum Citations | Maximum Citations |
|---|---|---|---|
| 1 | 0–20 | 0 | 1 |
| 2 | (20+1)–22 | 2 | 4 |
| 3 | (22+1)–23 | 5 | 8 |
| 4 | (23+1)–24 | 9 | 16 |
| 5 | (24+1)–25 | 17 | 32 |
| 6 | (25+1)–26 | 33 | 64 |
| 7 | (26+1)–27 | 65 | 128 |
| 8 | (27+1)–28 | 129 | 256 |
| 9 | (28+1)–29 | 257 | 512 |
| 10 | (29+1)–210 | 513 | 1024 |
| 11 | (210+1)–211 | 1025 | 2048 |
| 12 | (211+1)–212 | 2049 | 4096 |
| 13 | (212+1)–213 | 4097 | 8192 |
| 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) | 57 | 26 | 16 | 12 | 11 | 10 | 4 | 3 | 2 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
|---|
| Category (k) | Citation Range | Count of Pubs in Range (Pk) | kPk |
|---|---|---|---|
| 1 | 0–1 | 9 | 9 |
| 2 | 2–4 | 3 | 6 |
| 3 | 5–8 | 0 | 0 |
| 4 | 9–16 | 4 | 16 |
| 5 | 17–32 | 1 | 5 |
| 6 | 33–64 | 1 | 6 |
The index is the sum of kPk, thus CDS = 42.
History
| Year | CDS |
|---|---|
| 1997 | 6 |
| 1998 | 13 |
| 1999 | 21 |
| 2000 | 32 |
| 2001 | 42 |
| 2002 | 63 |
| 2003 | 83 |
| 2004 | 109 |
| 2005 | 133 |
| 2006 | 156 |
| 2007 | 175 |
| 2008 | 196 |
| 2009 | 208 |
| 2010 | 245 |
| 2011 | 268 |
| 2012 | 290 |
| 2013 | 306 |
| 2014 | 323 |
| 2015 | 349 |
| 2016 | 358 |
| 2017 | 370 |
| 2018 | 387 |
| 2019 | 400 |
| 2020 | 418 |
| 2021 | 435 |
| 2022 | 450 |
| 2023 | 464 |
| 2024 | 478 |
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.