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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Modeling Response Time Distributions with Generalized Beta Prime

Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 477--488 | 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 45221-0011

Department of Psychology, CAP Center for Cognition, Action, and Perception, University of Cincinnati, Cincinnati, Ohio 45221-0376

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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 power-law behavior at both front and tail ends and is a steady-state 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 scale-independent 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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