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Bounds and Inequalities Relating h-Index, g-Index, e-Index and Generalized Impact Factor: An Improvement over Existing Models

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  • Ash Mohammad Abbas

Abstract

In this paper, we describe some bounds and inequalities relating -index, -index, -index, and generalized impact factor. We derive the bounds and inequalities relating these indexing parameters from their basic definitions and without assuming any continuous model to be followed by any of them. We verify the theorems using citation data for five Price Medalists. We observe that the lower bound for -index given by Theorem 2, , comes out to be more accurate as compared to Schubert-Glanzel relation for a proportionality constant of , where is the number of citations and is the number of papers referenced. Also, the values of -index obtained using Theorem 2 outperform those obtained using Egghe-Liang-Rousseau power law model for the given citation data of Price Medalists. Further, we computed the values of upper bound on -index given by Theorem 3, , where denotes the value of -index. We observe that the upper bound on -index given by Theorem 3 is reasonably tight for the given citation record of Price Medalists.

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  • Ash Mohammad Abbas, 2012. "Bounds and Inequalities Relating h-Index, g-Index, e-Index and Generalized Impact Factor: An Improvement over Existing Models," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-7, April.
    • Handle: RePEc:plo:pone00:0033699
    DOI: 10.1371/journal.pone.0033699
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    References listed on IDEAS

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    1. Leo Egghe & Liming Liang & Ronald Rousseau, 2009. "A relation between h‐index and impact factor in the power‐law model," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 60(11), pages 2362-2365, November.
    2. Schubert, András & Glänzel, Wolfgang, 2007. "A systematic analysis of Hirsch-type indices for journals," Journal of Informetrics, Elsevier, vol. 1(3), pages 179-184.
    3. Chun-Ting Zhang, 2009. "The e-Index, Complementing the h-Index for Excess Citations," PLOS ONE, Public Library of Science, vol. 4(5), pages 1-4, May.
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