Content Vol. 3 N 12, 2017

Pages 252 - 263

Comparison of Gini’s Concentration Ratio between Pareto and Truncated Pareto Distribution; G. Venkatesan, R. Selvam* and V. Ayyandurai; Inter. J. Acad. Stud; 3(12):252-263.

The Pareto probability distribution is a simple model for a non-negative data with positively skewed distribution. It is widely used in different fields such as finance, economics, commerce, physics, geology etc,. This note deals with an application of Pareto distribution in the field of demography and more precisely to the statistical analysis of measures of variability of size of geographical areas. Since, the changes in size and structure of an area are random and skewed in nature, the Pareto model is proposed in this article. In particular a comparison of the Gini’s concentration ratio between Pareto and the truncated Pareto distribution is presented. Finally it was found that the Gini’s concentration ratio based on urban population in 2011 Census for the Pareto and truncated Pareto models were respectively ρ=0.1926 and ρ=0.7754 is greater than in 2001 Census for the Pareto and truncated Pareto models  respectively ρ=0.1356 and ρ=0.3538. This indicates that the urban population in 2011Census has more concentration than in 2001 Census at district level in Tamil Nadu State as per 2001 and 2011 Census data. It also showed that Gini’s concentration ratio is invariant under truncation only for the Pareto model and it is the best model than the truncated Pareto model.

Key words:
District size distribution, Gini’s concentration ratio, Invariant, Maximum Likelihood Estimation, Pareto model, Truncation-invariant, Truncated Pareto model.

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