random_cauchy_walk: Generate Multiple Random Cauchy Walks in Multiple Dimensions

In RandomWalker: Generate Random Walks Compatible with the 'tidyverse'

Generate Multiple Random Cauchy Walks in Multiple Dimensions

Description

The random_cauchy_walk function generates multiple random walks in 1, 2, or 3 dimensions. Each walk is a sequence of steps where each step is a random draw from a Cauchy distribution. The user can specify the number of walks, the number of steps in each walk, and the parameters of the Cauchy distribution (location and scale). The function also allows for sampling a proportion of the steps and optionally sampling with replacement.

Usage

random_cauchy_walk(
  .num_walks = 25,
  .n = 100,
  .location = 0,
  .scale = 1,
  .initial_value = 0,
  .samp = TRUE,
  .replace = TRUE,
  .sample_size = 0.8,
  .dimensions = 1
)

Arguments

.num_walks	An integer specifying the number of random walks to generate. Default is 25.
.n	An integer specifying the number of steps in each walk. Default is 100.
.location	A numeric value indicating the location parameter of the Cauchy distribution. Default is 0.
.scale	A numeric value indicating the scale parameter of the Cauchy distribution. Default is 1.
.initial_value	A numeric value indicating the initial value of the walks. Default is 0.
.samp	A logical value indicating whether to sample the Cauchy distribution values. Default is TRUE.
.replace	A logical value indicating whether sampling is with replacement. Default is TRUE.
.sample_size	A numeric value between 0 and 1 specifying the proportion of .n to sample. Default is 0.8.
.dimensions	An integer specifying the number of dimensions (1, 2, or 3). Default is 1.

Details

The location and scale parameters can be single values or vectors of length equal to the number of dimensions. If vectors are provided, each dimension uses its corresponding value.

Value

A tibble containing the generated random walks with columns depending on the number of dimensions:

• walk_number: Factor representing the walk number.

• step_number: Step index.

• y: If .dimensions = 1, the value of the walk at each step.

• x, y: If .dimensions = 2, the values of the walk in two dimensions.

• x, y, z: If .dimensions = 3, the values of the walk in three dimensions.

The following are also returned based upon how many dimensions there are and could be any of x, y and or z:

• cum_sum: Cumulative sum of dplyr::all_of(.dimensions).

• cum_prod: Cumulative product of dplyr::all_of(.dimensions).

• cum_min: Cumulative minimum of dplyr::all_of(.dimensions).

• cum_max: Cumulative maximum of dplyr::all_of(.dimensions).

• cum_mean: Cumulative mean of dplyr::all_of(.dimensions).

The tibble includes attributes for the function parameters.

Author(s)

Steven P. Sanderson II, MPH

See Also

Other Generator Functions: brownian_motion(), discrete_walk(), geometric_brownian_motion(), random_beta_walk(), random_binomial_walk(), random_chisquared_walk(), random_displacement_walk(), random_exponential_walk(), random_f_walk(), random_gamma_walk(), random_geometric_walk(), random_hypergeometric_walk(), random_logistic_walk(), random_lognormal_walk(), random_multinomial_walk(), random_negbinomial_walk(), random_normal_drift_walk(), random_normal_walk(), random_poisson_walk(), random_smirnov_walk(), random_t_walk(), random_uniform_walk(), random_weibull_walk(), random_wilcox_walk(), random_wilcoxon_sr_walk()

Other Continuous Distribution: brownian_motion(), geometric_brownian_motion(), random_beta_walk(), random_chisquared_walk(), random_exponential_walk(), random_f_walk(), random_gamma_walk(), random_logistic_walk(), random_lognormal_walk(), random_normal_drift_walk(), random_normal_walk(), random_t_walk(), random_uniform_walk(), random_weibull_walk()

Examples

set.seed(123)
random_cauchy_walk()

set.seed(123)
random_cauchy_walk(.dimensions = 3, .location = c(0, 1, 2), .scale = c(1, 2, 3)) |>
  head() |>
  t()

RandomWalker documentation built on Aug. 19, 2025, 1:14 a.m.