More "Normal" Than Normal: Scaling Distributions and Complex Systems

One feature of many naturally occurring or engineered complex systems is tremendous variability in event sizes. To account for it, the behavior of these systems is often described using power law relationships or scaling distributions, which tend to be viewed as "exotic" because of their unusual properties (e.g., infinite moments). An alternate view is based on mathematical, statistical, and data-analytic arguments and suggests that scaling distributions should be viewed as "more normal than Normal". In support of this latter view that has been advocated by Mandelbrot for the last 40 years, we review in this paper some relevant results from probability theory and illustrate a powerful statistical approach for deciding whether the variability associated with observed event sizes is consistent with an underlying Gaussian-type (finite variance) or scaling-type (infinite variance) distribution. We contrast this approach with traditional model fitting techniques and dis...

• Type: Conference
• Year: 2004
• Where: WSC
• Authors: Walter Willinger, David Alderson, John C. Doyle, Lun Li
• Keywords: Complex Systems, Event Sizes, Modeling And Simulation, Tremendous Variability, WSC 2004