The Pareto-positive stable distribution: A new descriptive model for city size data

José María Sarabia () and Faustino Prieto

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 19, 4179-4191

Abstract: The Pareto-positive stable (PPS) distribution is introduced as a new model for describing city size data in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data, where zero and unimodality are possible, and the classical Pareto and Zipf distributions are included as a particular case. Expressions for the shape, moments and other descriptive probabilistic measures are given. Estimation methods are discussed and a simple graphical method for studying the adequacy of the data to model is given. Finally, we consider city size data for Spain for several different years. The new distribution is compared with three classical models: Pareto, lognormal and Tsallis distributions. In all the data sets considered, the PPS distribution outperforms the fits of these three previous distributions.

Keywords: Pareto distribution; Positive stable law; Lognormal distribution; Tsallis distribution; City size (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:19:p:4179-4191

DOI: 10.1016/j.physa.2009.06.047

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