Title: The Cumulative Advantage Function. A Mathematical Formulation Based on Conditional Expectations and Its Application to Scientometric Distributions
Authors: Glänzel, Wolfgang
Schubert, András
Issue Date: 1990
Publisher: Elsevier Science Publisher
Host Document: Informetrics 89/90 pages:139-147
Conference: 2nd International Conference on Bibliometrics, Scientometrics and Informetrics location:London (Canada) date:4-7 July 1989
Abstract: Cumulative advantage principle is a specific law underlying several social, particularly, bibliometric and scientometric processes. This phenomenon was described by single- and multiple-urn models (Price, 1976, Tague, 1981). A theoretical model for cumulative advantage growth was developed by Schubert and Glänzel (1984). This paper presents an exact measure of the cumulative advantage effect based on conditional expectations. For a given bibliometric random variable X (e.g. publication activity, citation rate) the cumulative advantage function is defined as mu(k ) = E((X-k)|(X-k)>=0)/E(X). The 'extent of advantage' i s studied on the basis of limit properties of this function. The behavior of mu(k) is discussed for the urn-model distributions, particularly for its most prominent representatives, the negative-binomial and the Waring distribution. The discussion is illustrated by several examples from bibliometric distributions.
ISBN: 0-444-88460-2
Publication status: published
KU Leuven publication type: IHb
Appears in Collections:Non-KU Leuven Association publications

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