| Description |
1 online resource |
| Series |
Springer complexity |
|
Understanding complex systems |
|
Springer complexity.
|
|
Understanding complex systems.
|
| Contents |
Intro -- Preface -- Acknowledgements -- Contents -- Notation -- 1 Introduction -- References -- 2 From Lognormal to Power -- 2.1 Geometric Evolution -- 2.2 Gaussian White Noise -- 2.3 Brownian Motions -- 2.4 Gaussian Motions -- 2.5 Gaussian Mean and Variance -- 2.6 Gaussian Stationary Velocities -- 2.7 Poisson-Process Limit -- 2.8 Outlook -- 2.9 Notes -- 2.10 Methods -- 2.10.1 Equation (2.8) -- 2.10.2 Equation (2.13) -- 2.10.3 A General Poisson-Process Limit-Law -- 2.10.4 The Power Poisson-Process Limit-Law -- References -- 3 Setting the Stage -- 3.1 The Poisson Law -- 3.2 Framework |
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3.3 Methods -- 3.3.1 Normal Limit for Poisson Random Variables -- 3.3.2 Chernoff Bounds for Poisson Random Variables -- 3.3.3 Reciprocation of mathcalE+ and mathcalE- -- References -- 4 Threshold Analysis -- 4.1 Mean Behavior -- 4.2 Asymptotic Behavior -- 4.3 Log-Log Behavior -- 4.4 Pareto Laws -- 4.5 Pareto Scaling -- 4.6 Truncated Weibull Laws -- 4.7 Weibull Laws -- 4.8 Outlook -- References -- 5 Hazard Rates -- References -- 6 Lindy's Law -- References -- 7 Order Statistics -- 7.1 Simulation -- 7.2 Statistics -- 7.3 Asymptotic Behavior -- 7.4 Zipf Laws -- 7.5 Ratios -- 7.6 Log-Ratios |
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7.7 Forward Motion -- 7.8 Backward Motion -- 7.9 Outlook -- 7.10 Methods -- 7.10.1 Simulation -- 7.10.2 Equations(7.3) and (7.4) -- 7.10.3 Equations(7.9) and (7.11) -- 7.10.4 Equations(7.12) and (7.14) -- 7.10.5 Equations (7.20) and (7.21) -- 7.10.6 Equations(7.22) and (7.24) -- References -- 8 Exponent Estimation -- References -- 9 Socioeconomic Analysis -- 9.1 Socioeconomic Perspective -- 9.2 Disparity Curve -- 9.3 Disparity-Curve Analysis -- 9.4 Lorenz Curves -- 9.5 Lorenz-Curves Analysis -- 9.6 Inequality Indices -- 9.7 Gini Index -- 9.8 Reciprocation Index -- 9.9 Summary -- 9.10 Methods |
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9.10.1 Equation (9.4) -- 9.10.2 Equation (9.5) -- References -- 10 Fractality -- 10.1 Scale Invariance -- 10.2 Perturbation Invariance -- 10.3 Symmetric Perturbations -- 10.4 Socioeconomic Invariance -- 10.5 Poor Fractality and Rich Fractality -- 10.6 Renormalization -- 10.7 Summary -- 10.8 Methods -- 10.8.1 Equations(10.1), (10.2), and (10.11) -- 10.8.2 Equations(10.3) and (10.4) -- 10.8.3 Equations(10.5) and (10.6) -- 10.8.4 Equations(10.7) and (10.8) -- References -- 11 Sums -- 11.1 One-Sided Lévy Law I -- 11.2 Symmetric Lévy Law I -- 11.3 Uniform Random Scattering |
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11.4 One-Sided Lévy Law II -- 11.5 Symmetric Lévy Law II -- 11.6 Summary -- 11.7 Methods -- 11.7.1 Equations(11.2) and (11.3) -- 11.7.2 Equations (11.5) and (11.6) -- References -- 12 Dynamics -- 12.1 Growth and Decay -- 12.2 Evolution -- 12.3 Vanishing and Exploding -- 12.4 Order Statistics -- 12.5 Beyond the Singularity -- 12.6 Summary -- 12.7 Methods -- References -- 13 Limit Laws -- 13.1 Limit Laws I -- 13.2 Limit Laws II -- 13.3 Limit Laws III -- 13.4 Limit Laws IV -- 13.5 Limit Laws V -- 13.6 Outlook -- 13.7 Methods -- 13.7.1 Preparation I -- 13.7.2 The Limit mathcalE+ via Eq. (13.5) |
| Summary |
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 |
| Bibliography |
Includes bibliographical references |
| Subject |
Mathematical statistics.
|
|
Mathematical statistics
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| Genre/Form |
Electronic books
|
| Form |
Electronic book
|
| ISBN |
9783030332358 |
|
3030332357 |
|
9783030332365 |
|
3030332365 |
|
