random_poisson_walk: Generate Multiple Random Poisson Walks

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

Generate Multiple Random Poisson Walks

Description

A Poisson random walk is a stochastic process in which each step is drawn from the Poisson distribution, commonly used for modeling count data. 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 lambda parameter for the distribution. 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_poisson_walk(
  .num_walks = 25,
  .n = 100,
  .lambda = 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	Integer. Number of random variables to return for each walk. Default is 100.
.lambda	Numeric or vector. Mean(s) for the Poisson distribution. Default is 1.
.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_poisson_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 Poisson distribution using base::rpois(). The user can specify the number of samples in each walk (n), the lambda parameter for the Poisson distribution, 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_negbinomial_walk(), random_normal_drift_walk(), random_normal_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_negbinomial_walk(), random_smirnov_walk(), random_wilcox_walk(), random_wilcoxon_sr_walk()

Examples

set.seed(123)
random_poisson_walk()

set.seed(123)
random_poisson_walk(.dimensions = 3, .lambda = c(1, 2, 3)) |>
   head() |>
   t()

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