A rigorous analysis of Bradford's law is made using an index for the observed values of the variables. Three important properties relating size and frequency are identified. Using this approach, the shape of Bradford-type curves can be described in terms of three distinct regions and two shape parameters.
Authors:Ye-Sho Chen, P. Pete Chong and Yueguo Tong
A rigorous analysis of the 80/20 rule is made using an index for the observed values of the variables. Three important findings are identified. First, a sufficient condition is provided for Burrell's inverse relationship between minimum holdings and average circulation rate. Second, an indexed version of Lotka's law is used to derive a sufficient condition for Egghe's finding on the 80/20 rule. Third, through the computer simulations of the Simon-Yule model of Lotka's law, we identify the entry rate of new holdings as well as the number of circulations when the entry rate is a decreasing function to be crucial factors for the pattern of the 80/20-type curve.