  We present a simple generalization of Hirsch's h-index, Z =
\sqrt{h^{2}+C}/\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.
