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The size distributions of all Indian cities

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  • Luckstead, Jeff
  • Devadoss, Stephen
  • Danforth, Diana

Abstract

We apply five distributions–lognormal, double-Pareto lognormal, lognormal-upper tail Pareto, Pareto tails-lognormal, and Pareto tails-lognormal with differentiability restrictions–to estimate the size distribution of all Indian cities. Since India contains numerous small cities, it is important to explicitly model the lower-tail behavior for studying the distribution of all Indian cities. Our results rigorously confirm, using both graphical and formal statistical tests, that among these five distributions, Pareto tails-lognormal is a better suited parametrization of the Indian city size data, verifying that the Indian city size distribution exhibits a strong reverse Pareto in the lower tail, lognormal in the mid-range body, and Pareto in the upper tail.

Suggested Citation

  • Luckstead, Jeff & Devadoss, Stephen & Danforth, Diana, 2017. "The size distributions of all Indian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 237-249.
  • Handle: RePEc:eee:phsmap:v:474:y:2017:i:c:p:237-249
    DOI: 10.1016/j.physa.2017.01.065
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    References listed on IDEAS

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    3. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
    4. Lang, Wei & Long, Ying & Chen, Tingting & Li, Xun, 2019. "Reinvestigating China’s urbanization through the lens of allometric scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1429-1439.
    5. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    6. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman, 2018. "Optimal threshold for Pareto tail modelling in the presence of outliers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 169-180.
    7. Ramos, Arturo, 2019. "Addenda to “Are the log-growth rates of city sizes distributed normally? Empirical evidence for the USA [Empir. Econ. (2017) 53:1109-1123]”," MPRA Paper 93032, University Library of Munich, Germany.
    8. Arturo, Ramos, 2019. "Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century," MPRA Paper 93562, University Library of Munich, Germany.
    9. Gualandi, Stefano & Toscani, Giuseppe, 2019. "Size distribution of cities: A kinetic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 221-234.
    10. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & Hussain, Saiful Izzuan, 2019. "A robust and efficient estimator for the tail index of inverse Pareto distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 431-439.
    11. Biró, T.S. & Néda, Z., 2018. "Unidirectional random growth with resetting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 335-361.

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