Partial derivatives for the first-passage time distribution in Wiener diffusion models

The Wiener diffusion model with two absorbing barriers is frequently used in modeling decisions and decision latencies jointly. We derive representations of the partial derivatives of the density and cumulative distribution function of first-passage times. Different representations, based on infinite series, differ in convergence for small and large times, and we provide methods that control the approximation errors. These methods and their implementation in an R package are helpful whenever gradient information is required as is the case in many frequentist and Bayesian approaches to modeling. •Partial derivatives of the first-passage time PDF and CDF of the diffusion model are derived.•Small-time and large-time expressions enable fast computation for given approximation error.•An R package for computing these partial derivatives is provided and tested.