I-index: An objective measure for a researcher's share in the collective impact of his/her published papers

A researcher collaborating with many groups will normally have more papers (and thus higher citations and $h$-index) than a researcher spending all his/her time working alone or in a small group. While analyzing an author's research merit, it is therefore not enough to consider only the collective impact of the published papers, it is also necessary to quantify his/her share in the impact. For this quantification, here I propose the $I$-index which is defined as an author's percentage share in the total citations that his/her papers have attracted. It is argued that this $I$-index does not directly depend on the most of the subjective issues like an author's influence, affiliation, seniority or career break. A simple application of the Central Limit Theorem shows that, the scheme of equidistribution of credit among the co-authors of a paper will give us the most probable value of the $I$-index (with an associated small standard deviation which decreases with increasing $h$-index). I show that the total citations ($N_c$), the $h$-index and the $I$-index are three independent parameters (within their bounds), and together they give a comprehensive idea of an author's overall research merit.