Applications of the generalized law of Benford to informetric data

In a previous work (Egghe, 2011), the first author showed that Benfordʹs law (describing the logarithmic distribution of the numbers 1, 2, … , 9 as first digits of data in decimal form) is related to the classical law of Zipf with exponent 1. The work of Campanario and Coslado (2011), however, shows that Benfordʹs law does not always fit practical data in a statistical sense. In this article, we use a generalization of Benfordʹs law related to the general law of Zipf with exponent β > 0. Using data from Campanario and Coslado, we apply nonlinear least squares to determine the optimal β and show that this generalized law of Benford fits the data better than the classical law of Benford.