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 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

Auteur
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.

Résumé

"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)

Contenu
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.