The accuracy of graphs to describe size distributions

Abstract

This  article analyses the performance of the graphs traditionally used to study size distributions: histograms, Zipf plots (double logarithmic graphs of rank compared to size) and plotted cumulative density functions. A lognormal distribution is fitted to urban data from three countries (the United States, Spain and Italy) over all of the twentieth century. We explain the advantages and disadvantages associated with these graphic methods and derive some statistical properties.

Keywords:

• city size distribution
• Zipf plot
• lognormal

JEL Classification:

• C16
• R00

Acknowledgements

The authors acknowledge financial support from the Spanish Ministerio de Educación y Ciencia (ECO2009-09332 and ECO2010-16934 projects), the DGA (ADETRE research group), FEDER and the Generalitat (2009SGR102). This article includes part of the research contained in a working paper that circulated under the title ‘Size distributions for all cities: lognormal and q-exponential functions’. The results of this research have been presented at the XIII Encuentro de Economía Aplicada (Seville, 2010), at the 57th North American Meetings of the Regional Science Association International (Denver, 2010), at the XXXV Simposio de Análisis Económico (Madrid, 2010) and at the 51st Congress of the European Regional Science Association (Barcelona, 2011), with all the comments made by the participants being highly appreciated.

Notes

¹  More information about the databases and comparisons between these countries can be found in González-Val et al. (2013a).

²  The results, not shown for size restrictions, are available from the authors on request.

³  The results for the decades not shown are available from the authors on request.

⁴  See Fig. 2(b). The divergence between and is noticeable for (in the horizontal axis) lower than, say, 7, and from that value the differences are negligible.