Estimating parameters of the Pareto distribution by means of Zipf´s law: application to Internet research

A new estimation method for the Pareto distribution has been proposed. We have proved that a random variable that obeys Zipf´s law is Pareto distributed and shown how the parameters of the Pareto distribution can be determined by applying the Zipf´s law linear regression model. The maximum likelihood estimators of the Pareto distribution are given for comparison. Goodness of both fits is evaluated in terms of the Kolmogorov-Smirnov supremum statistic. The differences between numerical values of the Pareto distribution parameters determined by the proposed new method and the maximum likelihood estimation are investigated and explained. Three sets of actual measurement data are processed to illustrate how the presented new estimation algorithm can be applied in practice for Internet research.