Theoretical foundation of the 80/20 rule

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.