# dst0WienerPDF: Partial derivative of the first-passage time probability... In WienR: Derivatives of the Diffusion Density and Cumulative Distribution Function

## Description

Calculates the partial derivative of the first-passage time probability density function of the diffusion model with respect to the inter-trial variability of the non-decision time st0.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```dst0WienerPDF( t, response, a, v, w, t0 = 0, sv = 0, sw = 0, st0, 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 partial derivative. Numeric value. Default is `NULL`, which takes default value 1e-12. `K` Optional numeric value. 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_deriv` containing

• `deriv`: the derivatives of the PDF with respect to a,

• `call`: the function call,

• `err`: the absolute error.

Raphael Hartmann

## Examples

 `1` ```dst0WienerPDF(t = 1.2, response = "upper", a = 1.1, v = 13, w = .6, st0 = .2) ```

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