03133nam 22006735 450 991037395030332120250610110449.03-030-33235-710.1007/978-3-030-33235-8(CKB)4900000000505199(DE-He213)978-3-030-33235-8(MiAaPQ)EBC6114527(PPN)242845517(MiAaPQ)EBC29093146(EXLCZ)99490000000050519920191125d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierPower Laws A Statistical Trek /by Iddo Eliazar1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (XX, 203 p. 1 illus.) Understanding Complex Systems,1860-0840Includes index.3-030-33234-9 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.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.Understanding Complex Systems,1860-0840Mathematical physicsStatisticsDynamicsNonlinear theoriesSystem theoryTheoretical, Mathematical and Computational PhysicsStatistical Theory and MethodsApplied Dynamical SystemsComplex SystemsMathematical physics.Statistics.Dynamics.Nonlinear theories.System theory.Theoretical, Mathematical and Computational Physics.Statistical Theory and Methods.Applied Dynamical Systems.Complex Systems.519.5519.5Eliazar Iddoauthttp://id.loc.gov/vocabulary/relators/aut843579MiAaPQMiAaPQMiAaPQBOOK9910373950303321Power Laws1982530UNINA