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Une famille de distributions : des paretiennes aux « contra-paretiennes »

Applications à l'étude de la concentration urbaine et de son évolution
A family of distributions: from paretian to “contra-paretian”. Applications to the study of urban concentration and its evolution
Marc Barbut


We define a family of statistical distributions using a common functional equation they satisfy; this family includes Pareto's distribution, the exponential distribution and a “contra-paretian” distribution.
A very simple method for fitting these theoretical distributions to empirical data is briefly presented, and applied - with many details, and some success - to the rank-size distribution of French cities, during the 19th and 20th centuries, and its temporal evolution.

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Editor's notes

Cet article est paru dans Math. Inf. Sci. hum. (36e année, n° 141, 1998, pp. 43-72).


Electronic reference

Marc Barbut, « Une famille de distributions : des paretiennes aux « contra-paretiennes » », Cybergeo: European Journal of Geography [Online], Systems, Modelling, Geostatistics, document 266, Online since 25 March 2004, connection on 19 January 2022. URL : ; DOI :

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About the author

Marc Barbut


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Licence Creative Commons
La revue Cybergeo est mise à disposition selon les termes de la Licence Creative Commons Attribution 4.0 International.

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