A growth process for Zipf's and Yule's city-size laws
The Zipf rank - size law and the Yule probability laware both used to describe city populations. Though these laws are usually treated as identical, they describe city populations in different ways. These differences are first resolved, and the Zipf law is expressed in terms of the Yule law. Then urban growth is formulated by a probabilistic model as a pure birth process that generates city populations asymptotically obeying the Yule probability law. This model has similarities with the derivation by Yule of the law named after him and with the urban-growth model described in a well-known paper by Simon.
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