@article{eprints2376,
            year = {2013},
           title = {The Z-index: A geometric representation of productivity and impact which accounts for information in the entire rank-citation profile},
          number = {4},
           pages = {823--832},
           month = {October},
          volume = {7},
          author = {Alexander M. Petersen and Sauro Succi},
       publisher = {Elsevier},
         journal = {Journal of Informetrics},
        keywords = {Science of science; Citation impact; Rank stability; h-Index},
             url = {http://eprints.imtlucca.it/2376/},
        abstract = {We present a simple  generalization of Hirsch's h-index, Z {$\backslash$}equiv {$\backslash$}sqrt\{h{\^{ }}\{2\}+C\}/{$\backslash$}sqrt 5, where C is the total number of citations. Z is aimed at correcting  the potentially excessive penalty made by h on a scientist's highly cited papers, because for the majority of scientists analyzed, we find the excess citation fraction (C-h{\^{ }}\{2\})/C  to be distributed closely around the value 0.75, meaning that 75 percent of the author's impact is neglected. Additionally, Z is less sensitive to local changes in a scientist's citation profile, namely perturbations  which increase h while only marginally affecting C. Using real career data for 476 physicists careers and 488 biologist careers, we analyze both the distribution of Z and the rank stability of Z with respect to the Hirsch index h and the Egghe index g. We analyze careers distributed across a wide range of total impact, including top-cited physicists and biologists for benchmark comparison. In practice, the Z-index requires the same information needed to calculate h and could be effortlessly  incorporated within career profile 
databases, such as Google Scholar and ResearcherID. Because Z incorporates information from the entire publication profile while being more robust than h and g to local perturbations, we argue that Z is better suited for ranking comparisons in academic  decision-making scenarios comprising a large number of scientists. }
}