Modeling Response Time Distributions with Generalized Beta Prime

TL;DR

This paper introduces the use of the Generalized Beta Prime distribution to model response time data, demonstrating its flexibility and superior fit in distinguishing cognitive differences between groups such as children with dyslexia and controls.

Contribution

It applies the GB2 distribution to response time modeling, showing its effectiveness and flexibility in capturing distributional features and differences between groups.

Findings

GB2 provides superior fit to response time data.

Differences in scale and shape parameters reflect cognitive variability.

Distributional analysis reveals group differences in response dynamics.

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 can mimic 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.