random_multinomial_walk: Generate Multiple Random Multinomial Walks

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

Generate Multiple Random Multinomial Walks

Description

A multinomial random walk is a stochastic process in which each step is drawn from the multinomial distribution. This function allows for the simulation of multiple independent random walks in one, two, or three dimensions, with user control over the number of walks, steps, trials, probabilities, and dimensions. Sampling options allow for further customization, including the ability to sample a proportion of steps and to sample with or without replacement. The resulting data frame includes cumulative statistics for each walk.

Usage

random_multinomial_walk(
  .num_walks = 25,
  .n = 100,
  .size = 3,
  .prob = rep(1/3, .n),
  .initial_value = 0,
  .samp = TRUE,
  .replace = TRUE,
  .sample_size = 0.8,
  .dimensions = 1
)

Arguments

.num_walks	Integer. Number of random walks to generate. Default is 25.
.n	Integer. Length of each walk (number of steps). Default is 100.
.size	Integer. Number of trials for each multinomial draw. Default is 3.
.prob	Numeric vector. Probabilities for each outcome. Default is rep(1/3, .n).
.initial_value	Numeric. Starting value of the walk. Default is 0.
.samp	Logical. Whether to sample the steps. Default is TRUE.
.replace	Logical. Whether sampling is with replacement. Default is TRUE.
.sample_size	Numeric. Proportion of steps to sample (0-1). Default is 0.8.
.dimensions	Integer. Number of dimensions (1, 2, or 3). Default is 1.

Details

The random_multinomial_walk function generates multiple random walks using the multinomial distribution via stats::rmultinom(). Each walk is a sequence of steps where each step is a random draw from the multinomial distribution. The user can specify the number of walks, steps, trials per step, and the probability vector. Sampling options allow for further customization, including the ability to sample a proportion of steps and to sample with or without replacement. The resulting data frame includes cumulative statistics for each walk, making it suitable for simulation studies and visualization.

Value

A tibble containing the generated random walks with columns:

• walk_number: Factor representing the walk number.

• step_number: Step index.

• value: Value of the walk at each step.

• Cumulative statistics: cum_sum, cum_prod, cum_min, cum_max, cum_mean.

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).

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_cauchy_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_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 Discrete Distribution: discrete_walk(), random_binomial_walk(), random_displacement_walk(), random_geometric_walk(), random_hypergeometric_walk(), random_negbinomial_walk(), random_poisson_walk(), random_smirnov_walk(), random_wilcox_walk(), random_wilcoxon_sr_walk()

Examples

set.seed(123)
random_multinomial_walk()

set.seed(123)
random_multinomial_walk(.dimensions = 3) |>
  head() |>
  t()

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