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rank-size rule

  An empirical regularity in the city-size distributions of countries and regions. In its most general form, if the cities are rank-ordered according to their populations from the largest (1) to the smallest (n), then the population of the city ranked k can be derived from:

{img src=show_image.php?name=bkhumgeofm19.gif }

where Pk is the population of the city ranked k and P1 is the population of the largest city. The form of the relationship between Pk and k is J-shaped, but is linear if both are transformed logarithmically (see transformation of variables).

The precise relationship is usually identified empirically using regression analysis of the form:

{img src=show_image.php?name=bkhumgeofm20.gif }

The larger the value of b, the steeper the slope and thus the larger the city P1 relative to all others. (In the \'pure\' formulation, b = 1.0.)

No convincing explanation for the existence of the relationship has been developed, despite the frequency with which it is observed. Nor are there convincing explanations for the varying size of b (see also primate city, the law of the). (RJJ)

Suggested Reading Carroll, G.R. 1982: National city-size distributions: what do we know after 67 years of research? Progress in Human Geography 16: 1-43.



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