Template-Type: ReDIF-Paper 1.0
Title: Auerbach, Lotka, Zipf - pioneers of power-law city-size distributions
Author-Name: Diego Rybski
Author-Email: ca-dr@rybski.de
Author-Name: Antonio Ciccone
Author-Email: antonio.ciccone@uni-mannheim.de
Classification-JEL: B00, R12
Keywords: zipf's law for cities, empirical city size distributions 

Abstract: Power-law city-size distributions are a statistical regularity researched in many countries and
urban systems. In this history of science treatise we reconsider Felix Auerbach's paper published in
1913. We review his analysis and find (i) that a constant absolute concentration, as introduced by
him, is equivalent to a power-law distribution with exponent ≈ 1, (ii) that Auerbach describes this
equivalence, and (iii) that Auerbach also pioneered the empirical analysis of city-size distributions
across countries, regions, and time periods. We further investigate his legacy as reflected in citations
and find that important follow-up work, e.g. A.J. Lotka 1925 and Zipf 1949, does give proper
reference to his discovery - but other does not. For example, only approximately 20% of cityrelated
works citing Zipf 1949 also cite Auerbach 1913. To our best knowledge, A.J. Lotka 1925
was the first to describe the power-law rank-size rule as it is analyzed today. M. Saibante 1928,
building on Auerbach and Lotka, investigated the power-law rank-size rule across countries, regions,
and time periods. G.K. Zipf's achievement was to embed these findings in his monumental 1949
book. We suggest that the use of "Auerbach-Lotka-Zipf law" (or "ALZ-law") is more appropriate
than "Zipf's law for cities", which also avoids confusion with Zipf's law for word frequency. We end
the treatise with biographical notes on Auerbach.

Note: 
Length: 6
Creation-Date: 2023-05
Revision-Date: 
File-URL: https://www.crctr224.de/research/discussion-papers/archive/dp424
File-Format: application/pdf
Handle: RePEc:bon:boncrc:CRCTR224_2023_424