# gradWienerCDF: Gradient of the first-passage time cumulative distribution... In WienR: Derivatives of the First-Passage Time Density and Cumulative Distribution Function, and Random Sampling from the (Truncated) First-Passage Time Distribution

## Gradient of the first-passage time cumulative distribution function

### Description

Calculates the gradient of the first-passage time cumulative distribution function.

### Usage

t,
response,
a,
v,
w,
t0,
sv,
sw,
st0,
precision = NULL,
K = NULL,
n.evals = 6000
)

### 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. 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. n.evals 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.

### Value

A list of the class Diffusion_deriv containing

• deriv: the derivatives of the CDF with respect to a, v, w, t0, sv, sw, and st0,

• 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

Hartmann, R., & Klauer, K. C. (2021). Partial derivatives for the first-passage time distribution in Wiener diffusion models. Journal of Mathematical Psychology, 103, 102550. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmp.2021.102550")}

### Examples

gradWienerCDF(t = 1.2, response = "upper", a = 1.1, v = 13, w = .6,
t0 = .3, sv = .1, sw = .1, st0 = .1)

WienR documentation built on July 9, 2023, 5:16 p.m.