Statistical analysis of urbanization and an application towards a Pareto model

Abstract

Background: India is only 23.7 percent urban at the present time and this cannot be considered a high level of urbanization. However, when we look at the number of people living in the cities (around 156 million out of the total population of 684 million in 1981) the significance of urban population assumes importance. Aims and objective: To fit Pareto model to the urban population data of Tamil Nadu state and to compare the urbanization in Tamil Nadu over the 3 decades (1981, 1991, 2001). Materials and method: we were collected three years Indian census population data of Tamil Nadu state (1981, 1991, and 2001) As city size models are in skew nature the Pareto model has been fitted to the Tamil Nadu population data for the above said three years and the fitness of the model were tested using chi-square statistics. Result: The estimates of the parameters a, k for the years 1981, 1991 and 2001 are 1.784, 6039.4224, 1.3901, 5807.60 and 1.79572, 6688.082, the χ2 –statistics for the years 1981, 1991 and 2001 are 171.64, 104.737 and 304.819, i.e., for all the three years the χ2 0.05 < χ2 calculated value hence the Pareto model is not good fit for the all the population data. Conclusion: The city size distribution is skewed distributions. The less variation between the observed and expected number of cities in all the 3 years. Thus the Pareto model may be proposed and we found that the Pareto model is not a good fit for all the population data.