weighted citation aggregate (proportional)
The proportional weighted citation aggregate (Abbas 2011) is a weighted count of an author's citations (an alternative to total citations), where the weighting is based on the total number of authors of each publication and their position within the author list (ai) under an assumption of proportionally decreasing credit with respect to their position.
$$\psi_p=\sum\limits_{i=i}^{P}{\frac{C_i}{\frac{A_i\left(A_i+1\right)}{2\left(A_i+1-a_i\right)}}}=\sum\limits_{i=i}^{P}{C_i\frac{2\left(A_i+1-a_i\right)}{A_i\left(A_i+1\right)}}$$History
Year | ψp |
---|---|
1997 | 0.7000 |
1998 | 5.9000 |
1999 | 16.2000 |
2000 | 34.4000 |
2001 | 64.2333 |
2002 | 117.9556 |
2003 | 190.4706 |
2004 | 290.2933 |
2005 | 420.1210 |
2006 | 604.6568 |
2007 | 809.5759 |
2008 | 1006.5019 |
2009 | 1229.4567 |
2010 | 1498.6864 |
2011 | 1851.0170 |
2012 | 2146.8089 |
2013 | 2508.2832 |
2014 | 2809.0019 |
2015 | 3123.6985 |
2016 | 3459.6043 |
2017 | 3757.0368 |
2018 | 4076.0667 |
2019 | 4392.0258 |
2020 | 4711.5888 |
2021 | 5059.9772 |
2022 | 5415.5295 |
2023 | 5738.1899 |
2024 | 6056.2709 |
References
- Abbas, A.M. (2011) Weighted indices for evaluating the quality of research with multiple authorship. Scientometrics 88:107–131.