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weighted citation H-cut (proportional)

The proportional weighted citation H-cut is the sum of weighted citations found within an author's core publications, with the core defined by the position-weighted h-indexand the citation weighting using the scheme from the weighted citation aggregate (proportional):

$$\xi_p=\sum\limits_{i=1}^{h_p}{C^{*}_i}=\sum\limits_{i=i}^{h_p}{\frac{C_i}{\frac{A_i\left(A_i+1\right)}{2\left(A_i+1-a_i\right)}}}=\sum\limits_{i=i}^{h_p}{C_i\frac{2\left(A_i+1-a_i\right)}{A_i\left(A_i+1\right)}}.$$

Note that for this metric publication order is by the weighted citation counts rather than the raw citation counts.

Example

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

Citations (Ci)591111162631041113200000
Authors (Ai)313231441124442111
Author Position (ai)111231311113331111
Author Effort (Ei)0.501.000.500.330.171.000.200.401.001.000.670.200.200.200.671.001.001.00
Weight (wi)2.001.002.003.006.001.005.002.501.001.001.505.005.005.001.501.001.001.00
Adjusted Citations (\(C^*_i\))29.5011.005.505.334.333.002.001.601.001.000.670.600.400.000.000.000.000.00
Rank (i)123456789101112131415161718
hp = 4

The sum of the adjusted citations for the top hp publications is 51.333333333333336.

History

Yearξp
19970.0000
19983.5000
199911.6667
200026.6667
200151.3333
200298.1667
2003153.5000
2004238.1667
2005357.5238
2006499.5833
2007682.5595
2008883.4048
20091082.1548
20101346.3452
20111665.0238
20121935.7348
20132283.5379
20142576.3766
20152852.3496
20163173.9232
20173433.1645
20183706.9037
20194012.2900
20204331.7946
20214677.9439
20224997.9781
20235331.3398
20245640.9766
20255827.1320

References