Distribution in the geometrically growing system and its evolution

Recently, we developed a theory of a geometrically growing system. Here, we show that the theory can explain some phenomena of power-law distribution, including classical demographic and economic and novel instances of the COVID-19 pandemic, without introduction of delicate economic or pandemic propagation models but only on a statistical way. A convexity in the low-size part of the distribution diagram is one peculiarity of the theory, which is absent in the power-law distribution. We found that the distribution of the geometrically growing system in the diagram could have a trend to flatten in the evolution of the system so that the relative ratio between the biggest and smallest sizes within the system increases. The system can act as a reverse machine to convert the diffusion in parametric space to a concentration in size.