On the classification of the classical bibliometric laws

Abstract

It is well known that the laws of Leimkuhler, Mandelbrot, Lotka and the verbal formulation of Bradford's law are equivalent. In this note we prove an analogous framework of laws in which now the law of Zipf occurs instead of Mandelbrot's law. Laws in this group are Brookes' law and the graphical formulation of Bradford's law. We show that both groups of laws are very different in the sense that they are not even equal asymptotically for high rankings.