Power Laws

This monograph is a comprehensive and cohesive exposition of power-law statistics. Following a bottom-up construction from a foundational bedrock the power Poisson process this monograph presents a unified study of an assortment of power-law statistics including: Pareto laws, Zipf laws, Weibull and Frchet laws, power Lorenz curves, Lvy laws, power Newcomb-Benford laws, sub-diffusion and super-diffusion, and 1/f and flicker noises. The bedrock power Poisson process, as well as the assortment of power-law statistics, are investigated via diverse perspectives: structural, stochastic, fractal, dynamical, and socioeconomic. This monograph is poised to serve researchers and practitioners from various fields of science and engineering that are engaged in analyses of power-law statistics.