# WienerPDF: First-passage time probability density function of the... In WienR: Derivatives of the Diffusion Density and Cumulative Distribution Function

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```WienerPDF( t, response, a, v, w, t0 = 0, sv = 0, sw = 0, st0 = 0, precision = NULL, K = NULL, n.threads = FALSE ) ```

## Arguments

 `t` First-passage time. Numeric vector. `response` Response boundary. Character vector with `"upper"` and `"lower"` as possible values. Alternatively a numeric vector with `1`=lower and `2`=upper. `a` Upper barrier. Numeric vector. `v` Drift rate. Numeric vector. `w` Relative starting point. Numeric vector. `t0` Non-decision time. Numeric vector `sv` Inter-trial variability of drift rate. Numeric vector. Standard deviation of a normal distribution `N(v, sv)`. `sw` Inter-trial variability of relative starting point. Numeric vector. Range of uniform distribution `U(w-0.5*sw, w+0.5*sw)`. `st0` Inter-trial variability of non-decision time. Numeric vector. Range of uniform distribution `U(t0, t0+st0)`. `precision` Optional numeric value. Precision of the PDF. Numeric value. Default is `NULL`, which takes default value 1e-12. `K` 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`. `n.threads` 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.

## Value

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

## References

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/j.jmp.2014.05.002

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/j.jmp.2009.02.003

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

## Examples

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

WienR documentation built on May 12, 2021, 1:08 a.m.