The power-law distribution is common in the nature world and our social life. In the field of Information Science, the Lotka's Law, which describes the scientific productivity, and the Zipf's Law, which describes
Is is shown, using rigorous statistical tests, that the number of journals (J) carryingp papers in a given subject can be expressed as a simple power law functionJ(p)=K p–, K and being constants. The standard maximum likelihood method of estimating has been suitably modified to take acoount of the fact thatp is a discrete integer variable. The parameter entirely characterises the scatter of articles in journals in a given bibliography. According to a dynamic model proposed earlier by the author, is a measure of the relative growth rates of papers and journals pertaining to the subject.
A relation, established by András Schubert (Scientometrics 78(3): 559–565, 2009) on the relation between a paper’s h-index
and its total number of received citations, is explained. The relation is a concavely increasing power law and is explained
based on the Lotkaian model for the h-index, proved by Egghe and Rousseau.
Authors:Y. Zhang, K. Ma, M. Anand, W. Ye, and B. Fu
Alpha, beta, and gamma diversity are three fundamental biodiversity components in ecology, but most studies focus only on the scale issues of the alpha or gamma diversity component. The beta diversity component, which incorporates both alpha and gamma diversity components, is ideal for studying scale issues of diversity. We explore the scale dependency of beta diversity and scale relationship, both theoretically as well as by application to actual data sets. Our results showed that a power law exists for beta diversity-area (spatial grain or spatial extent) relationships, and that the parameters of the power law are dependent on the grain and extent for which the data are defined. Coarse grain size generates a steeper slope (scaling exponent z) with lower values of intercept (c), while a larger extent results in a reverse trend in both parameters. We also found that, for a given grain (with varying extent) or a given extent (with varying grain) the two parameters are themselves related by power laws. These findings are important because they are the first to simultaneously relate the various components of scale and diversity in a unified manner.
Lack of standard procedures hinders progress in scientometric and bibliometric research. Provoked by a recent publication in the journal Scientometrics, we consider in particular the problem of how to handle - in a standardised way - data that, by and large, follow a Lotka, Zipf or Mandelbrot distribution
count of articles.
Powerlaw analysis methodology
A persistent pattern associated with complex system is powerlaws. In bibliometrics, powerlaws are commonly seen in publication frequencies (Lotka 1926 ), citation
Authors:Pedro Albarrán, Juan A. Crespo, Ignacio Ortuño, and Javier Ruiz-Castillo
citation distributions can be represented by powerlaws (see Egghe 2005 , for a treatise on the importance of powerlaws for information production processes of which citation distributions are only one type). More recently, in two important contributions