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.
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
distribution, but on a log–log scale. This distribution appears to be nearly linear. This is the characteristic signature of a power-law distribution. It is reported that most of the real-world networks including the World Wide Web (Huberman and Adamic 1999
taggers and IO professionals. Up until now, three different approaches have been adopted to study the use of social tags in the IO domain. Several studies have examined whether use of social tags generally follows a power-law distribution (Angus et al
b . The reason is that the productivity of the journals itself (not the cumulative rank-frequency distribution) follows an inverse powerlaw y = g / x h with g = 25,500 and h = 0.38 in the area of the most productive journals (for the rank x