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 Fréchet laws, power Lorenz curves, Lévy 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.
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.
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"A suitable book for both theoretical scholars and practitioners. The formal aspects are rigorously, and elegantly, presented and complex mathematical tools are always used to clarify and ease the reading. ... we strongly recommend the reading of this comprehensive and well written monograph a book that should not be missing in the libraries of Departments of Mathematics and Statistics, and that may be of interest to both experienced researchers and practitioners." (Giovanni Maria Giorgi, METRON, April 9, 2021)