Blurton, Steven Paul4; Kesselmeier, M.5; Gondan, Matthias4
1 Institut for Psykologi, Department of Psychology, Faculty of Social Sciences, Københavns Universitet2 Department of Psychology, Faculty of Social Sciences, Københavns Universitet3 University of Heidelberg4 Institut for Psykologi, Department of Psychology, Faculty of Social Sciences, Københavns Universitet5 University of Heidelberg
We propose an improved method for calculating the cumulative first-passage time distribution in Wiener diffusion models with two absorbing barriers. This distribution function is frequently used to describe responses and error probabilities in choice reaction time tasks. The present work extends related work on the density of first-passage times [Navarro, D.J., Fuss, I.G. (2009). Fast and accurate calculations for first-passage times in Wiener diffusion models. Journal of Mathematical Psychology, 53, 222-230]. Two representations exist for the distribution, both including infinite series. We derive upper bounds for the approximation error resulting from finite truncation of the series, and we determine the number of iterations required to limit the error below a pre-specified tolerance. For a given set of parameters, the representation can then be chosen which requires the least computational effort.
Journal of Mathematical Psychology, 2012, Vol 56, Issue 6, p. 470-475