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The Pareto-Positive Stable(PPS) distribution is introduced as a new model for describing city size data of a region in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data and the classical Pareto and Zipf distributions are included as a particular case. The new distribution is compared with two classical models: Pareto and lognormal distribution. In all the data sets considered, the Newtons forward and backward(equal intervals), Lagrange interpolation formula(unequal interval) outperforms the fits of Pareto and lognormal distributions.

THE SIZE DISTRIBUTION OF CITIES IN A REGION: AN EVALUATION OF PARETO, LOGNORMAL AND PPS DISTRIBUTIONS