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On the Rank‐Size Distribution for Human Settlements
Author(s) -
Reed William J.
Publication year - 2002
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/1467-9787.00247
Subject(s) - log normal distribution , rank (graph theory) , mathematics , settlement (finance) , pareto principle , pareto distribution , distribution (mathematics) , parametric statistics , econometrics , statistics , statistical physics , economics , combinatorics , physics , mathematical analysis , finance , payment
An explanation for the rank‐size distribution for human settlements based on simple stochastic models of settlement formation and growth is presented. Not only does the analysis of the model explain the rank‐size phenomenon in the upper tail, it also predicts a reverse rank‐size phenomenon in the lower tail. Furthermore it yields a parametric form (the double Pareto‐lognormal distribution) for the complete distribution of settlement sizes. Settlement‐size data for four regions (two in Spain and two in the U.S.) are used as examples. For these regions the lower tail rank‐size property is seen to hold and the double Pareto‐lognormal distribution shown to provide an excellent fit, lending support to the model and to the explanation for the rank‐size law.