Discontinuity, Nonlinearity, and Complexity
Modeling Response Time Distributions with Generalized Beta Prime
Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 477488  DOI:10.5890/DNC.2020.09.009
M. Dashti Moghaddam, Jiong Liu, John G. Holden, R. A. Serota
Department of Physics, University of Cincinnati, Cincinnati, Ohio 452210011
Department of Psychology, CAP Center for Cognition, Action, and Perception, University of Cincinnati, Cincinnati, Ohio 452210376
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Abstract
We use Generalized Beta Prime distribution, also known as GB2, for fitting response time distributions. This distribution, characterized by one scale and three shape parameters, is incredibly flexible in that it canmimic behavior of many other distributions. GB2 exhibits powerlaw behavior at both front and tail ends and is a steadystate distribution of a simple stochastic differential equation. We apply GB2 in contrast studies between two distinct groups – in this case children with dyslexia and a control group – and
show that it provides superior fitting. We compare aggregate response time distributions of the two groups for scale and shape differences (including several scaleindependent measures of variability, such as Hoover index), which may in turn reflect on cognitive dynamics differences. In this approach, response time distribution of an individual can be considered as a random variate of that individual’s group distribution.
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