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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)472619151110432111100000

Category
(k)
Citation
Range
Count of Pubs
in Range
(Pk)
kPk
10–199
22–436
35–800
49–16312
517–32210
633–6416

The index is the sum of kPk, thus CDS = 43.

History

YearCDS
19976
199813
199920
200030
200143
200263
200385
2004109
2005134
2006156
2007176
2008196
2009208
2010244
2011267
2012288
2013305
2014324
2015350
2016359
2017368
2018389
2019402
2020417
2021434
2022450
2023465
2024467

References