The Geometric and the Bradford Distributions: A Comparison

Abstract

Both the geometric and the Bradford probability distributions are used to describe collections of items of interest in information science. Each unit item has a productivity, an integer n measuring the amount of use of the item. The cumulative fraction Fn of items with productivity equal to n or greates may be expressed as a function of n or else as a function of the cumulative mean productivity Gn of items with productivity equal to n or greater. If Fn is an exponential function of n, the distribution is geometric; if it is an exponential function of Gn, it is a Bradford distribution. The exact solution of Fn as a function of n for the Bradford distribution is computed; the results are tabulated. Graphs are given, comparing the two distributions, and their relative usefulness is discussed.