Physics – Physics and Society
Scientific paper
2011-01-31
Physics
Physics and Society
Scientific paper
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.
Hisano Ryohei
Mizuno Takayuki
Sornette Didier
No associations
LandOfFree
Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-647396