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.

Presents an in-depth exposition of the power Poisson process Highlights many applications including a socioeconomic analysis Introduces the reader to all the statistical forms with inherent power structures

Autorentext
Iddo Eliazar is an avid multi-disciplinary explorer of randomness, with about 150 scientific research publications on Operations Research, Stochastic Modeling, Statistical Physics, Econo-Physics and Socio-Physics. In academia, he held senior faculty positions at Tel Aviv University, at Bar Ilan University, and at the Holon Institute of Technology. In industry, he served as a Research Scientist at Intel's New Devices Group, and as a Section Head at Bank Hapoalim's Department of Analytic Development. Dr. Eliazar holds the following degrees from Tel-Aviv University: BSc in Mathematics and Statistics (Summa Cum Laude), MSc in Operations Research (Summa Cum Laude), and PhD.

Inhalt
Introduction.- From lognormal to power.- The Poisson law.- Framework.- Threshold analysis.- Hazard rates.- Order statistics.- Exponent estimation.- Socioeconomic analysis.- Fractality.- Sums.- Dynamics.- Limit laws.- First digits.- Back to lognormal.- Conclusion.- Appendix.