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Untangling Herdan's law and Heaps' law: Mathematical and informetric arguments

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  • Leo Egghe

Abstract

Herdan's law in linguistics and Heaps' law in information retrieval are different formulations of the same phenomenon. Stated briefly and in linguistic terms they state that vocabularies' sizes are concave increasing power laws of texts' sizes. This study investigates these laws from a purely mathematical and informetric point of view. A general informetric argument shows that the problem of proving these laws is, in fact, ill‐posed. Using the more general terminology of sources and items, the author shows by presenting exact formulas from Lotkaian informetrics that the total number T of sources is not only a function of the total number A of items, but is also a function of several parameters (e.g., the parameters occurring in Lotka's law). Consequently, it is shown that a fixed T (or A) value can lead to different possible A (respectively, T) values. Limiting the T(A)‐variability to increasing samples (e.g., in a text as done in linguistics) the author then shows, in a purely mathematical way, that for large sample sizes T≈LAθ, where θ is a constant, θ6

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  • Leo Egghe, 2007. "Untangling Herdan's law and Heaps' law: Mathematical and informetric arguments," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(5), pages 702-709, March.
    • Handle: RePEc:bla:jamist:v:58:y:2007:i:5:p:702-709
    DOI: 10.1002/asi.20524
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    Cited by:

    1. Espitia, Diego & Larralde, Hernán, 2020. "Universal and non-universal text statistics: Clustering coefficient for language identification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    2. Wei, Shelia X. & Tong, Tong & Rousseau, Ronald & Wang, Wanru & Ye, Fred Y., 2022. "Relations among the h-, g-, ψ-, and p-index and offset-ability," Journal of Informetrics, Elsevier, vol. 16(4).
    3. Egghe, L., 2013. "The functional relation between the impact factor and the uncitedness factor revisited," Journal of Informetrics, Elsevier, vol. 7(1), pages 183-189.
    4. Franceschini, Fiorenzo & Galetto, Maurizio & Maisano, Domenico & Mastrogiacomo, Luca, 2013. "An informetric model for the success-index," Journal of Informetrics, Elsevier, vol. 7(1), pages 109-116.
    5. Anna Tietze & Philip Hofmann, 2019. "The h-index and multi-author hm-index for individual researchers in condensed matter physics," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(1), pages 171-185, April.

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