Per capita wealth in cities and regions fitted to Pareto, stretched exponential and econophysics Boltzmann–Gibbs distributions

Abstract

From the years 2001 to 2017, per capita nominal and real (adjusted to inflation) GDP at purchasing power parity (PCGDP-PPP) distributions for cities and regions are fitted to various functions. For most years and regions, real PCGDP-PPP data are very well adjusted to the one-parameter Boltzmann–Gibbs distribution (BGD), in accordance with the exponential behavior predicted by the simple econophysics analogy between conserved money in economic trade and energy in elastic collisions in gases. Overall, fittings are better for large regions in recent years, which may reflect an increasing economic globalization in time. Cities, small regions and large regions values are well fitted by stretched exponential distributions.

Impact of Regional Differences in Risk Attitude on the Power Law at the Urban Scale

“…Its probability density function is y = c x-a, which represents the proportional relationship -a between scale y and frequency x [30]. Various power law characteristics exist in the real world, such as the distributions of drainage structure [31], population wealth [32,33], paper frequency [34], and the urban system. The rank-size rule from Zipf in 1949 proved that the urban scale and their ranks had linear characteristics under double logarithmic values.…”