WienerCDF: First-passage time cumulative distribution function of the...

In WienR: Derivatives of the First-Passage Time Density and Cumulative Distribution Function, and Random Sampling from the (Truncated) First-Passage Time Distribution

First-passage time cumulative distribution function of the diffusion model

Description

Calculates the first-passage time cumulative distribution function of the diffusion model.

Usage

WienerCDF(
  t,
  response,
  a,
  v,
  w,
  t0 = 0,
  sv = 0,
  sw = 0,
  st0 = 0,
  precision = NULL,
  K = NULL,
  n.threads = FALSE,
  n.evals = 6000
)

pWDM(
  t,
  response,
  a,
  v,
  w,
  t0 = 0,
  sv = 0,
  sw = 0,
  st0 = 0,
  precision = NULL,
  K = NULL,
  n.threads = FALSE,
  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 CDF. 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_cdf containing

• cdf: the CDF,

• logcdf: the log-transformed CDF,

• 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.

Author(s)

Raphael Hartmann

References

Blurton, S. P., Kesselmeier, M., & Gondan, M. (2012). Fast and accurate calculations for cumulative first-passage time distributions in Wiener diffusion models. Journal of Mathematical Psychology, 56(6), 470–475. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmp.2012.09.002")}

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmp.2014.05.002")}

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

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

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