Leo Egghe

Classification of growth models based on growth rates and its applications

In this paper, growth models are classified and characterised using two types of growth rates: from time t to t+1 and from time t to 2t. They are interesting in themselves but can also be used for a quick prediction of the type of growth model that is valid in a particular case. These ideas are applied on 20 data sets collected byWolfram, Chu andLu. We determine (using the above classification as well as via nonlinear regression techniques) that the power model (with exponent>1) is the best growth model for Sci-Tech online databases, but that Gompertz-S-shaped distribution is the best for social sciences and humanities online databases.

Citation age data and the obsolescence function: Fits and explanations

LOUVAIN UNIV CATHOLIC,B-3590 DIEPENBEEK,BELGIUM. RV COLL,CTR DOCUMENTAT RES & TRAINING,BANGALORE 560059,INDIA.EGGHE, L, UNIV INSTELLING ANTWERP,UNIV PLEIN 1,B-2610 WILRIJK,BELGIUM.

A heuristic study of the first-citation distribution

The first-citation distribution, i.e. the cumulative distribution of the time period between publication of an article and the time it receives its first citation, has never been modelled by using well-known informetric distributions. An attempt to this is given in this paper. For the diachronous aging distribution we use a simple decreasing exponential model. For the distribution of the total number of received citations we use a classical Lotka function. The combination of these two tools yield new first-citation distributions.

On the influence of growth on obsolescence

In many papers, the influence of growth on obsolescence is studied but a formal model for such an influence has not been constructed. In this paper, we develop such a model and find different results for the synchronous and for the diachronous study. We prove that, in the synchronous case, an increase of growth implies an increase of the obsolescence, while, in the diachronous case, exactly the opposite mechanism is found. Exact proofs are given, based on the exponential models for growth as well as obsolescence. We leave open a more general theory.

Applications of the theory of Bradford's Law to the calculation of Leimkuhler's Law and to the completion of bibliographies

In a previous article (L. Egghe, JASIS 37(4); p. 246–255, 1986) we further developed the theory of Bradfords law by deriving a theoretical formula for the Bradford multiplier and for the number of items, produced by the most productive source in every Bradford group. In this article we apply these results to some classical bibliographies, for which we determine the underlying law of Leimkuhler and also different Bradford groupings. We also extend the above mentioned theory in order to be applicable to incomplete bibliographies (s.a. citation tables or bibliographies truncated before the Groos droop). Finally this extension also has an application in determining the size and other properties of the complete unknown bibliography, based on the incomplete one.

Average and global impact of a set of journals

In this note we clarify some notions concerning citations, publications, and their quotients: impact and indifference (a measure of invisibility, introduced in this article). In particular, we show that the slope of the regression line of the impact as a function of the number of publications is positive if and only if the global impact, i.e. the impact of the set of all journals under consideration, is larger than the average impact of all journals.

Mathematical derivation of the impact factor distribution

Experimental data [Mansilla, R., Koppen, E., Cocho, G., & Miramontes, P. (2007). On the behavior of journal impact factor rank-order distribution. Journal of Informetrics, 1(2), 155–160] reveal that, if one ranks a set of journals (e.g. in a field) in decreasing order of their impact factors, the rank distribution of the logarithm of these impact factors has a typical S-shape: first a convex decrease, followed by a concave decrease. In this paper we give a mathematical formula for this distribution and explain the S-shape. Also the experimentally found smaller convex part and larger concave part is explained. If one studies the rank distribution of the impact factors themselves, we now prove that we have the same S-shape but with inflection point in μ, the average of the impact factors. These distributions are valid for any type of impact factor (any publication period and any citation period). They are even valid for any sample average rank distribution.

On the 80/20 rule

In a recent paper1Burrell shows that libraries with lower average borrowings tend to require a larger proportion of their collections to account for 80% of the borrowings, than those with higher average borrowings. In that study, the underlying frequency distribution was a negative binomial. We are dealing with a case when the underlying distribution is of Lotka type. It is also shown that the “80/20-effect” is much stronger in this case.

The Distribution of N-Grams

AbstractN-grams are generalized words consisting of N consecutive symbols, as they are used in a text. This paper determines the rank-frequency distribution for redundant N-grams. For entire texts this is known to be Zipfs law (i.e., an inverse power law). For N-grams, however, we show that the rank (r)-frequency distribution is