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

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  • Sarabia, José María
  • Prieto, Faustino

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.

Suggested Citation

  • Sarabia, José María & Prieto, Faustino, 2009. "The Pareto-positive stable distribution: A new descriptive model for city size data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4179-4191.
  • Handle: RePEc:eee:phsmap:v:388:y:2009:i:19:p:4179-4191
    DOI: 10.1016/j.physa.2009.06.047
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Sáez, Antonio José & Prieto, Faustino & Sarabia, José María, 2012. "A two-tail version of the PPS distribution with application to current account balance data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5160-5171.
    2. Sarabia, José María & Prieto, Faustino & Trueba, Carmen & Jordá, Vanesa, 2013. "About the modified Gaussian family of income distributions with applications to individual incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1398-1408.
    3. Calderín-Ojeda, Enrique, 2016. "The distribution of all French communes: A composite parametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 385-394.
    4. Francisco Louzada & Daniele C. T. Granzotto, 2016. "The transmuted log-logistic regression model: a new model for time up to first calving of cows," Statistical Papers, Springer, vol. 57(3), pages 623-640, September.
    5. Sen, Hu & Chunxia, Yang & Xueshuai, Zhu & Zhilai, Zheng & Ya, Cao, 2015. "Distributions of region size and GDP and their relation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 46-56.
    6. Kii, Masanobu & Akimoto, Keigo & Doi, Kenji, 2012. "Random-growth urban model with geographical fitness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5960-5970.
    7. Gómez-Déniz, Emilio & Calderín-Ojeda, Enrique, 2015. "On the use of the Pareto ArcTan distribution for describing city size in Australia and New Zealand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 821-832.

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