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The Z-index: A geometric representation of productivity and impact which accounts for information in the entire rank-citation profile

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  • Petersen, Alexander M.
  • Succi, Sauro

Abstract

We present a simple generalization of Hirsch's h-index, Z≡h2+C/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−h2)/C to be distributed closely around the value 0.75, meaning that 75% 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.

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  • Petersen, Alexander M. & Succi, Sauro, 2013. "The Z-index: A geometric representation of productivity and impact which accounts for information in the entire rank-citation profile," Journal of Informetrics, Elsevier, vol. 7(4), pages 823-832.
    • Handle: RePEc:eee:infome:v:7:y:2013:i:4:p:823-832
    DOI: 10.1016/j.joi.2013.07.003
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    1. Rossi, Luciano & Freire, Igor L. & Mena-Chalco, Jesús P., 2017. "Genealogical index: A metric to analyze advisor–advisee relationships," Journal of Informetrics, Elsevier, vol. 11(2), pages 564-582.
    2. Oscar Fontanelli & Pedro Miramontes & Yaning Yang & Germinal Cocho & Wentian Li, 2016. "Beyond Zipf’s Law: The Lavalette Rank Function and Its Properties," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-14, September.
    3. Letchford, Adrian & Preis, Tobias & Moat, Helen Susannah, 2016. "The advantage of simple paper abstracts," Journal of Informetrics, Elsevier, vol. 10(1), pages 1-8.
    4. Fabio Zagonari, 2019. "Scientific Production and Productivity for Characterizing an Author’s Publication History: Simple and Nested Gini’s and Hirsch’s Indexes Combined," Publications, MDPI, vol. 7(2), pages 1-30, May.

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