Generate Multiple Random Multinomial Walks

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.

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.

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.

See also

Other Generator Functions: brownian_motion(), discrete_walk(), geometric_brownian_motion(), 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_hypergeometric_walk(), random_negbinomial_walk(), random_poisson_walk(), random_smirnov_walk(), random_wilcox_walk(), random_wilcoxon_sr_walk()

Author

Steven P. Sanderson II, MPH

Examples

set.seed(123)
random_multinomial_walk()
#> # A tibble: 2,000 × 8
#>    walk_number step_number     y cum_sum_y cum_prod_y cum_min_y cum_max_y
#>    <fct>             <int> <int>     <dbl>      <dbl>     <dbl>     <dbl>
#>  1 25                    1     0         0          0         0         0
#>  2 25                    2     0         0          0         0         0
#>  3 25                    3     0         0          0         0         0
#>  4 25                    4     0         0          0         0         0
#>  5 25                    5     0         0          0         0         0
#>  6 25                    6     0         0          0         0         0
#>  7 25                    7     1         1          0         0         1
#>  8 25                    8     0         1          0         0         1
#>  9 25                    9     0         1          0         0         1
#> 10 25                   10     0         1          0         0         1
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>

set.seed(123)
random_multinomial_walk(.dimensions = 3) |>
  head() |>
  t()
#>             [,1] [,2] [,3] [,4] [,5] [,6]
#> walk_number "25" "25" "25" "25" "25" "25"
#> step_number "1"  "2"  "3"  "4"  "5"  "6" 
#> x           "0"  "0"  "0"  "0"  "0"  "0" 
#> y           "0"  "0"  "0"  "0"  "0"  "0" 
#> z           "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_sum_x   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_sum_y   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_sum_z   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_prod_x  "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_prod_y  "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_prod_z  "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_min_x   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_min_y   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_min_z   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_max_x   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_max_y   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_max_z   "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_mean_x  "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_mean_y  "0"  "0"  "0"  "0"  "0"  "0" 
#> cum_mean_z  "0"  "0"  "0"  "0"  "0"  "0"