A study of rank distributions of journals and articles

Two bibliographies (one in mathematics and the other one in Physics) are analyzed to study the relation among the journals, references and the citations as well as both the rank and size distributions of citations. It has been observed that the number of citations (z) received by a journal can be estimated using a log model i.e. z = ay - by log (y) (Basu's Model); y is the number of references in a subject in x most journals. Further, it has been observed that Basu's model with two free parameters (a and b), y = ax - bx log (x), fits very well to the observed data on the rank distribution of articles, where y is the citations received by the x most productive articles. It has also been observed that the size distribution of citations follows a negative binomial distribution, implying that the distribution of citations in a bibliography is a manifestation of success-breeds-success phenomenon. The Spearman rank correlation coefficient for the data on rank distributions of journals (based on articles and citations) is only 0.0972515, indicating that the ranks are quite different from each other; however, among the top 10 journals, 9 journals are common in both the ranked list. However, this is not true for the group consisting of least productive journals.