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 Newtons forward and backward(equal intervals), Lagrange interpolation formula(unequal interval) outperforms the fits of Pareto and lognormal distributions.
Highlights
In this work we have analyzed the city size distribution data using the methodology viz., PPS distribution developed by Sarabia and Prieto(2009)
In this paper we have considered the models evolved by Sarabia and Prieto (2009)
For purposes we have considered lognormal distribution and Pareto distribution for fitting City Size Distribution data
Summary
In this work we have analyzed the city size distribution data using the methodology viz., PPS distribution developed by Sarabia and Prieto(2009). Pareto distribution was initially proposed Auerbach(1913) and followed by Zipf(1949) to fit City size data. Sarabia and Prieto(2009) have stated that the validity of the Pareto distribution disappears when all the population is fitted, including cities of medium and small size. The descriptive model evolved by them is called PPS distribution for city/town size data. The PPS distribution provides a flexible model for fitting the entire range of a set of city/town size data, when zero and uni-modelity are possible. The probability density function always decreases or it has a local maximum
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