2011/01/31 by Ryohei Hisano, Didier Sornette, Takayuki Mizuno · 10 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · Social Sciences · #Birth–death process #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Econometrics #Evolutionary Game Theory and Cooperation #Exponent #Mathematics #Physics #Power law #Statistical physics #Statistics #Universality (dynamical systems) #Zipf's law #cs.SI #physics.soc-ph
paper · pdf · doi:10.1103/physreve.84.026117
published in Physical Review E 84(2), 026117 (American Physical Society)
arxiv created 2011/07/28 · openalex publication_date 2011/08/24 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional growth, and (ii) birth and death processes, leads to a generic power-law distribution with an exponent that depends on the characteristics of each ingredient. Here, we report the first complete empirical test of the theory and its application, based on the empirical analysis of the dynamics of market shares in the product market. We estimate directly the average growth rate of market shares and its standard deviation, the birth rates and the "death" (hazard) rate of products. We find that temporal variations and product differences of the observed power-law exponents can be fully captured by the theory with no adjustable parameters. Our results can be generalized to many systems for which the statistical properties revealed by power-law exponents are directly linked to the underlying generating mechanism.