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Malevergne, Y., Pisarenko, V. and Sornette, D. (2011) Testing the Pareto against the Lognormal Distributions with the Uniformly Most Powerful Unbiased Test Applied to the Distribution of Cities. Physical Review E, 83, Article ID: 036111.
https://doi.org/10.1103/PhysRevE.83.036111

has been cited by the following article:

• TITLE: Non-Maxwellian Kinetic Modelling of City Size Distribution

  AUTHORS: Lijuan Yu, Jie Liao

  KEYWORDS: Variable Collision Kernel, Kinetic Fokker-Planck Equation, Generalized Gamma Distribution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.9 No.6, June 28, 2021

  ABSTRACT: To extend the kinetic formulation of city size distribution introduced in [1], the non-Maxwellian kinetic modeling is introduced in the present study, in which a variable collision kernel is used in the underlying kinetic equation of Boltzmann type. By resorting to the well-known grazing asymptotic, a kinetic Fokker-Planck counterpart is obtained. The equilibrium of the Fokker-Planck equation belongs to the class of generalized Gamma distributions. Numerical test shows good fit of the generalized Gamma distribution with the city size distribution of China.