IJPAM: Volume 92, No. 2 (2014)

THE SIZE DISTRIBUTION OF CITIES IN A REGION:
AN EVALUATION OF PARETO, LOGNORMAL
AND PPS DISTRIBUTIONS

V. Christopher Amalraj$^1$, A. Subbarayan$^2$, S. Balamuralitharan$^3$
$^1$Department of Community Medicine
S.R.M. Medical College and Research Centre
Kattankulathur, 603 203, INDIA
$^2$Department of Computer Applications
S.R.M. University
Kattankulathur, 603 203, INDIA
$^3$Faculty of Engineering and Technology
Department of Mathematics
S.R.M. University
Kattankulathur, 603202, Tamil Nadu, INDIA


Abstract. The Pareto-Positive Stable(PPS) distribution is introduced as a new model for describing city size data of a region in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data and the classical Pareto and Zipf distributions are included as a particular case. The new distribution is compared with two classical models: Pareto and lognormal distribution. In all the data sets considered, the Newton’s forward and backward(equal intervals), Lagrange interpolation formula(unequal interval) outperforms the fits of Pareto and lognormal distributions.

Received: December 30, 2013

AMS Subject Classification: 62H10, 62H12

Key Words and Phrases: city-size distribution, Pareto distribution, Pareto Positive Stable law

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DOI: 10.12732/ijpam.v92i2.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 92
Issue: 2
Pages: 265 - 278

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).