-
Egghe, L.: Untangling Herdan's law and Heaps' law : mathematical and informetric arguments (2007)
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- 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~ A**phi, where phi is a constant, phi < 1 but close to 1, hence roughly, Heaps' or Herdan's law can be proved without using any linguistic or informetric argument. The author also shows that for smaller samples, a is not a constant but essentially decreases as confirmed by practical examples. Finally, an exact informetric argument on random sampling in the items shows that, in most cases, T= T(A) is a concavely increasing function, in accordance with practical examples.
- Source
- Journal of the American Society for Information Science and Technology. 58(2007) no.5, S.702-709
-
Egghe, L.; Ravichandra Rao, I.K.: ¬The influence of the broadness of a query of a topic on its h-index : models and examples of the h-index of n-grams (2008)
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- Abstract
- The article studies the influence of the query formulation of a topic on its h-index. In order to generate pure random sets of documents, we used N-grams (N variable) to measure this influence: strings of zeros, truncated at the end. The used databases are WoS and Scopus. The formula h=T**1/alpha, proved in Egghe and Rousseau (2006) where T is the number of retrieved documents and is Lotka's exponent, is confirmed being a concavely increasing function of T. We also give a formula for the relation between h and N the length of the N-gram: h=D10**(-N/alpha) where D is a constant, a convexly decreasing function, which is found in our experiments. Nonlinear regression on h=T**1/alpha gives an estimation of , which can then be used to estimate the h-index of the entire database (Web of Science [WoS] and Scopus): h=S**1/alpha, , where S is the total number of documents in the database.
- Source
- Journal of the American Society for Information Science and Technology. 59(2008) no.10, S.1688-1693
-
Egghe, L.; Rousseau, R.: ¬The Hirsch index of a shifted Lotka function and its relation with the impact factor (2012)
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- Abstract
- Based on earlier results about the shifted Lotka function, we prove an implicit functional relation between the Hirsch index (h-index) and the total number of sources (T). It is shown that the corresponding function, h(T), is concavely increasing. Next, we construct an implicit relation between the h-index and the impact factor IF (an average number of items per source). The corresponding function h(IF) is increasing and we show that if the parameter C in the numerator of the shifted Lotka function is high, then the relation between the h-index and the impact factor is almost linear.
- Source
- Journal of the American Society for Information Science and Technology. 63(2012) no.5, S.1048-1053
-
Egghe, L.; Guns, R.; Rousseau, R.; Leuven, K.U.: Erratum (2012)
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- Date
- 14. 2.2012 12:53:22
- Footnote
- This article corrects: Thoughts on uncitedness: Nobel laureates and Fields medalists as case studies in: JASIST 62(2011) no,8, S.1637-1644.
- Source
- Journal of the American Society for Information Science and Technology. 63(2012) no.2, S.429
-
Egghe, L.; Rousseau, R.: Averaging and globalising quotients of informetric and scientometric data (1996)
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- Source
- Journal of information science. 22(1996) no.3, S.165-170
-
Egghe, L.: ¬A universal method of information retrieval evaluation : the "missing" link M and the universal IR surface (2004)
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- Date
- 14. 8.2004 19:17:22
- Source
- Information processing and management. 40(2004) no.1, S.21-30
-
Egghe, L.: Little science, big science and beyond (1994)
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- Source
- Scientometrics. 30(1994) nos.2/3, S.389-392
-
Egghe, L.: Expansion of the field of informetrics : the second special issue (2006)
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- Source
- Information processing and management. 42(2006) no.6, S.1405-1407
-
Egghe, L.: Expansion of the field of informetrics : origins and consequences (2005)
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- Source
- Information processing and management. 41(2005) no.6, S.1311-1316
-
Egghe, L.: Special features of the author - publication relationship and a new explanation of Lotka's law based on convolution theory (1994)
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- Source
- Journal of the American Society for Information Science. 45(1994) no.6, S.422-427
-
Egghe, L.: Note on a possible decomposition of the h-Index (2013)
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- Source
- Journal of the American Society for Information Science and Technology. 64(2013) no.4, S.871
-
Egghe, L.: ¬The Hirsch index and related impact measures (2010)
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- Source
- Annual review of information science and technology. 44(2010) no.1, S.65-114
-
Egghe, L.: Informetric explanation of some Leiden Ranking graphs (2014)
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- Abstract
- The S-shaped functional relation between the mean citation score and the proportion of top 10% publications for the 500 Leiden Ranking universities is explained using results of the shifted Lotka function. Also the concave or convex relation between the proportion of top 100?% publications, for different fractions ?, is explained using the obtained new informetric model.
- Source
- Journal of the Association for Information Science and Technology. 65(2014) no.4, S.737-741
-
Egghe, L.: ¬A good normalized impact and concentration measure (2014)
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- Journal of the Association for Information Science and Technology. 65(2014) no.10, S.2052-2054
-
Egghe, L.; Rousseau, R.; Rousseau, S.: TOP-curves (2007)
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- Source
- Journal of the American Society for Information Science and Technology. 58(2007) no.6, S.777-785
-
Egghe, L.: ¬A rationale for the Hirsch-index rank-order distribution and a comparison with the impact factor rank-order distribution (2009)
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- Abstract
- We present a rationale for the Hirsch-index rank-order distribution and prove that it is a power law (hence a straight line in the log-log scale). This is confirmed by experimental data of Pyykkö and by data produced in this article on 206 mathematics journals. This distribution is of a completely different nature than the impact factor (IF) rank-order distribution which (as proved in a previous article) is S-shaped. This is also confirmed by our example. Only in the log-log scale of the h-index distribution do we notice a concave deviation of the straight line for higher ranks. This phenomenon is discussed.
- Source
- Journal of the American Society for Information Science and Technology. 60(2009) no.10, S.2142-2144
-
Egghe, L.; Guns, R.; Rousseau, R.: Thoughts on uncitedness : Nobel laureates and Fields medalists as case studies (2011)
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- Footnote
- Vgl.: Erratum. In: Journal of the American Society for Information Science and Technology. 63(2012) no.2, S.429.
- Source
- Journal of the American Society for Information Science and Technology. 62(2011) no.8, S.1637-1644
-
Egghe, L.: ¬The amount of actions needed for shelving and reshelving (1996)
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- Source
- Library management. 17(1996) no.1, S.18-24
-
Egghe, L.; Rousseau, R.: Duality in information retrieval and the hypegeometric distribution (1997)
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- Source
- Journal of documentation. 53(1997) no.5, S.499-496
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Egghe, L.: On the law of Zipf-Mandelbrot for multi-word phrases (1999)
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- Source
- Journal of the American Society for Information Science. 50(1999) no.3, S.233-241
