random_negbinomial_walk: Generate Multiple Random Negative Binomial Walks

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

Generate Multiple Random Negative Binomial Walks

Description

A Negative Binomial random walk is a stochastic process in which each step is drawn from the Negative Binomial distribution, commonly used for modeling count data with overdispersion. 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, and the distribution parameters. 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.

Usage

random_negbinomial_walk(
  .num_walks = 25,
  .n = 100,
  .size = 1,
  .prob = 0.5,
  .mu = NULL,
  .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	Integer. Number of random variables to return for each walk. Default is 100.
.size	Integer. Number of successful trials or dispersion parameter. Default is 1. This must also match the number of dimensions, for example if .dimensions = 3, then .size must be a vector of length 3 like c(1, 2, 3).
.prob	Numeric. Probability of success in each trial (0 < prob <= 1). Default is 0.5. This must also match the number of dimensions, for example if .dimensions = 3, then .prob must be a vector of length 3 like c(0.5, 0.7, 0.9).
.mu	Numeric. Alternative parametrization via mean. Default is NULL. This must also match the number of dimensions, for example if .dimensions = 3, then .mu must be a vector of length 3 like c(1, 2, 3).
.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_negbinomial_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 the Negative Binomial distribution using stats::rnbinom(). The user can specify the number of samples in each walk (n), the size parameter, the probability of success (prob), and/or the mean (mu), and the number of dimensions. The function also allows for sampling a proportion of the steps and optionally sampling with replacement.

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).

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_multinomial_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_multinomial_walk(), random_poisson_walk(), random_smirnov_walk(), random_wilcox_walk(), random_wilcoxon_sr_walk()

Examples

set.seed(123)
random_negbinomial_walk()

set.seed(123)
random_negbinomial_walk(.dimensions = 3,
  .size = c(1,2,3),
  .prob = c(0.5,0.7,0.9)
  ) |>
  head() |>
  t()

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