A new optimization parameter in a statistical sample !
I just thought up a new citation index parameter. Its very interesting check this out.
It reflects the quality scope of the citations. Its the total percentage of a citation that goes into defining a particular citation index. Let me call it q-index therefore (q for quality)
See this example.
My h-ind is 60. So total (minimum) citation it accounts for is 60*60 = 3600. My total citation is 12215. So my q-ind is 3600/12215 = 29.47% Or 29.47% of my total citation were important for this parameter. Hence my q-index is 29.47. In this way if someone has 5000 total citation with h-index 60, he has a much better q-index than mine, because more of his paper are highly cited. [his would be 72% vs mine 30%, we both have h-index 60 but his q-index is 72 and mine 30, considered for the same index-type; h.]
Now my i10-index is 174. It takes therefore 174*10 = 1740 out of 12215 citations. So quality is less. The q-index is now 1740/12215 = 14.24% or q-ind = 14.24.
See that my i10 index compared to my h-index is a low quality measure of my citations. While the number is bigger (174 > 60 ) the actual area of citation it covers is less.
Note that the q-index needs be corrected in the sense that the actual percentage will differ since some papers will have lets say 80 citations (in the h-index 60 list) and some will have 30 citation in the i10-ind list)
But for minimal considerations, h-ind 60 q-ind 29.47 says 30% at-least of total citations have been consequential. For i10 = 174 on the other hand only 14.24 % is consequential. When we have more info (which is available in determining h or i10) q-index tells us what percentage of citation indices are actually consequential.
One can then normalize different indices to a particular q-index value to say how to scale an index (h or i10 or g eg) to its q-index optimized value.
So if I scale the optimization of q to lets say 35% (because for different people/sample the q will differ, so I first scale everyone to a particular value) then I can compare the h-ind, i10 and g etc of different people or sample.
For person A h-ind is having a consequential quality of 30% and for person B its at 45% then they need to be re-normalized first? According to the q-index as a percentage of citations that have been counted. As simple as a b c ..