An Optimization-Based Generative Model of Power Laws Using a New Information Theory Based Metric

Abstract: In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this function are analyzed. The derived function shows some similarity to the entropy function in representing order and randomness; however, it also represents the energy, where the optimization process is seeking to maximize the number of elements at the tail of the distribution constrained by the total amount of the energy. The results show a matching between the output of the optimization process and the power law distribution.