WienerPDF: First-passage time probability density function of the...

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WienerPDFR Documentation

First-passage time probability density function of the diffusion model


Calculate the first-passage time probability density function of the diffusion model.


  t0 = 0,
  sv = 0,
  sw = 0,
  st0 = 0,
  precision = NULL,
  K = NULL,
  n.threads = FALSE,
  n.evals = 6000



First-passage time. Numeric vector.


Response boundary. Character vector with "upper" and "lower" as possible values. Alternatively a numeric vector with 1=lower and 2=upper.


Upper barrier. Numeric vector.


Drift rate. Numeric vector.


Relative starting point. Numeric vector.


Non-decision time. Numeric vector


Inter-trial variability of drift rate. Numeric vector. Standard deviation of a normal distribution N(v, sv).


Inter-trial variability of relative starting point. Numeric vector. Range of uniform distribution U(w-0.5*sw, w+0.5*sw).


Inter-trial variability of non-decision time. Numeric vector. Range of uniform distribution U(t0, t0+st0).


Optional numeric value. Precision of the PDF. Numeric value. Default is NULL, which takes default value 1e-12.


Optional. Number of iterations to calculate the infinite sums. Numeric value (integer). Default is NULL.

  • precision = NULL and K = NULL: Default precision = 1e-12 used to calculate internal K.

  • precision != NULL and K = NULL: precision is used to calculate internal K,

  • precision = NULL and K != NULL: K is used as internal K,

  • precision != NULL and K != NULL: if internal K calculated through precision is smaller than K, K is used.

We recommend using either default (precision = K = NULL) or only precision.


Optional numerical or logical value. Number of threads to use. If not provided (or 1 or FALSE) parallelization is not used. If set to TRUE then all available threads are used.


Optional. Number of maximal function evaluations in the numeric integral if sv, sw, and/or st0 are not zero. Default is 6000 and 0 implies no limit and the numeric integration goes on until the specified precision is guaranteed.


A list of the class Diffusion_pdf containing

  • pdf: the PDF,

  • logpdf: the log-transformed PDF,

  • call: the function call,

  • err: the absolute error. Only provided if sv, sw, or st0 is non-zero. If numerical integration is used, the precision cannot always be guaranteed.


Raphael Hartmann


Blurton, S. P., Kesselmeier, M., & Gondan, M. (2017). The first-passage time distribution for the diffusion model with variable drift. Journal of Mathematical Psychology, 76, 7–12. doi: 10.1016/

Foster, K., & Singmann, H. (2021). Another Approximation of the First-Passage Time Densities for the Ratcliff Diffusion Decision Model. arXiv preprint arXiv:2104.01902.

Gondan, M., Blurton, S. P., & Kesselmeier, M. (2014). Even faster and even more accurate first-passage time densities and distributions for the Wiener diffusion model. Journal of Mathematical Psychology, 60, 20–22. doi: 10.1016/

Hartmann, R., & Klauer, K. C. (2021). Partial derivatives for the first-passage time distribution in Wiener diffusion models. Journal of Mathematical Psychology, 103, 102550. doi: 10.1016/

Navarro, D. J., & Fuss, I. G. (2009). Fast and accurate calculations for first-passage times in Wiener diffusion models. Journal of Mathematical Psychology, 53(4), 222–230. doi: 10.1016/

Wabersich, D., & Vandekerckhove, J. (2014). The RWiener Package: an R Package Providing Distribution Functions for the Wiener Diffusion Model. The R Journal, 6(1), 49. doi: 10.32614/rj-2014-005


WienerPDF(t = 1.2, response = "upper", a = 1.1, v = 13, w = .6, precision = NULL, K = NULL)

WienR documentation built on April 23, 2022, 9:05 a.m.

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