Maximum likelihood estimator for Zipf distribution: a new approach

In this paper, an evaluation of the methodologies for the estimation of Zipf law parameters such as the least squares errors, maximum likelihood function and the approach by Clauset, Shalizi and Newmann (2007) is shown. The transformation technique for generating random numbers with genuine discrete Zipf distribution is employed and the parameters are estimated by the above techniques. According to the results the best performance for scale parameter was the maximum likelihood estimation. It exhibits values of the coefficient of determination around 0.99 for Zipf’s coefficient in the range of 0.5 and 3.0.