A type-token identity in the Simon-Yule model of text
Journal of the American Society for Information Science
The duality of informetric systems with applications to the empirical laws
Journal of Information Science
The duality of informatic systems with applications to the empirical laws
The duality of informatic systems with applications to the empirical laws
Block addressing indices for approximate text retrieval
Journal of the American Society for Information Science - Special topic issue: When museum informatics meets the World Wide Web
Information Retrieval: Computational and Theoretical Aspects
Information Retrieval: Computational and Theoretical Aspects
Distributive h-indices for measuring multilevel impact
Journal of the American Society for Information Science and Technology
Information Processing and Management: an International Journal
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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≈LA&thetas;, where &thetas; is a constant, &thetas;6T = T(A) is a concavely increasing function, in accordance with practical examples. © 2007 Wiley Periodicals, Inc.