Dresden 2009 – wissenschaftliches Programm

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AGSOE: Arbeitsgruppe Physik sozio-ökonomischer Systeme

AGSOE 8: Traffic Dynamics, Urban and Regional Systems II

AGSOE 8.5: Vortrag

Dienstag, 24. März 2009, 12:15–12:30, BAR 205

The Pareto-positive stable distribution: a descriptive model for city size data — •Jose Maria Sarabia and Faustino Prieto — University of Cantabria, Santander, Spain

The Pareto-positive stable (PPS) distribution is introduced as a new model for describing city size data in several countries. The PPS distribution provides a flexible model for fitting all the 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.

The new model has a twofold origin. Initially, it can be obtained by mixing the shape parameter of a classical Pareto distribution with a positive stable distribution. In this way we can model the possible heterogeneity in the set of city sizes. The distribution obtained is also genuine by extending the range of the characteristic exponent in the stable law. PPS distribution can be also obtained from a monotonic transformation of the classical Weibull distribution.

Probabilistic properties are studied and several descriptive measures are obtained. Maximum likelihood estimators are proposed. Initial estimators of the parameters can be obtained using regression methods. A simple graphical method for studying the adequacy of the data to model is given.

Finally, we consider city size data for USA and Spain for several years, because they are the countries with highest migration shocks in recent years. Some classical distributions as well as PPS distribution are fitted, and we conclude that PPS distribution outperforms previous models.