On the use of the Pareto ArcTan distribution for describing city size in Australia and New Zealand
Emilio Gomez-Deniz, Enrique Calderin-Ojeda
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | ELSEVIER SCIENCE BV | Published : 2015
The circular inverse of the tangent function is used to simply derive a generalization of the Pareto distribution, the Pareto ArcTan (PAT) distribution. This model includes as limiting cases Pareto and Zipf distributions. This new probabilistic family is used to describe city size data for Australia and New Zealand. Urban agglomerations of these two countries presents similar features, a few large metropolitan areas with a steadily increasing population in the last years and many small cities. The PAT distribution improves the performance of other traditionally used models in urban agglomeration economics such as the classical Pareto, lognormal and the recently proposed Pareto positive stabl..View full abstract
Awarded by Ministerio de Economia y Competitividad, Spain
The authors would like to express their gratitude to two anonymous referees and associate editor for their relevant and useful comments. Authors have been partially funded by grant ECO2013-47092 (Ministerio de Economia y Competitividad, Spain). EGD also acknowledges the Faculty of Business and Economics and the Centre of Actuarial Studies at the University of Melbourne for their special support, since part of this paper was written while EGD was visiting the University of Melbourne in July 2014.