Ranking techniques and the empirical log law

摘要

Four empirical laws of bibliometrics—those of anomalous numbers, of Lotka, Zipf and Bradford, together with Laplace's notorious “law of succession” and de Solla Price's cumulative advantage distribution, are shown to be almost identical. Some of these laws are expressed as frequency distributions, some are frequency-ranked. A simple model which discriminates these various forms is described. It shows that the frequency forms conform with an inverse square law over the appropriate interval and that the equivalent rank distribution—the Log Law—has the Df Q (r)=logb(r+l) where b is the rank interval. It is further shown that frequency distributions discard empirical statistical information which the equivalent rank distributions retain for analysis. So that rank distributions offer theoretical advantages in this field. The paper concludes with comments on the analysis of the empirical hybrid forms which arise. The reduction of the above laws, empirical and hypothetical, to a single law is achieved by NOT equating the ordinals 1st, 2nd, 3rd,…. to the numbers 1, 2, 3, 4. as is commonly done.