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THE SIZE DISTRIBUTION OF URBAN AREAS: TESTING FOR THE APPROPRIATENESS OF THE PARETO DISTRIBUTION USING A GENERALIZED BOX‐COX TRANSFORMATION FUNCTION *
Author(s) -
Alperovich Gershon,
Deutsch Joseph
Publication year - 1995
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/j.1467-9787.1995.tb01258.x
Subject(s) - pareto principle , transformation (genetics) , distribution (mathematics) , goodness of fit , generalized pareto distribution , function (biology) , reciprocal , econometrics , pareto distribution , power transform , mathematics , statistics , extreme value theory , mathematical analysis , discrete mathematics , biology , biochemistry , chemistry , linguistics , philosophy , consistency (knowledge bases) , evolutionary biology , gene
A widely held opinion among urban economists and geographers is that the Pareto distribution is an accurate representation of the urban size distribution of many countries around the world. This paper focuses attention on the appropriateness of the procedures used in the literature in arriving at this conclusion. We employed the generalized Box‐Cox transformation function, which permits estimation of many functional forms for testing the Pareto distribution as special cases. The results obtained are illuminating albeit somewhat surprising. Except for one country the Pareto distribution is overwhelmingly rejected in favor of the general Box‐Cox function. In more than 30 percent of all countries this form collapses to a reciprocal function. Moreover, as far as the overall goodness of fit is concerned, our results show that the General Box‐Cox function is superior to the Pareto form.