A fractal approach to dynamic inference and distribution analysis.
Event-distributions inform scientists about the variability and dispersion of repeated measurements. This dispersion can be understood from a complex systems perspective, and quantified in terms of fractal geometry. The key premise is that a distribution's shape reveals information about the governing dynamics of the system that gave rise to the distribution. Two categories of characteristic dynamics are distinguished: additive systems governed by component-dominant dynamics and multiplicative or interdependent systems governed by interaction-dominant dynamics. A logic by which systems governed by interaction-dominant dynamics are expected to yield mixtures of lognormal and inverse power-law samples is discussed. These mixtures are described by a so-called cocktail model of response times derived from human cognitive performances. The overarching goals of this article are twofold: First, to offer readers an introduction to this theoretical perspective and second, to offer an overview of the related statistical methods.
Department of Psychology, CAP Center for Cognition, Action, and Perception, University of Cincinnati Cincinnati, OH, USA.
Marieke M J W
MM
van Rooij
Bertha A
BA
Nash
Srinivasan
S
Rajaraman
John G
JG
Holden
cognitive performance; distribution analysis; dynamic systems; fractal analysis; response time distributions; scaling relations