Generate Multiple Random Wilcoxon Walks in Multiple Dimensions

The random_wilcox_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 Wilcoxon distribution using stats::rwilcox(). The user can specify the number of walks, the number of steps in each walk, and the parameters .m and .n for the Wilcoxon distribution. The function also allows for sampling a proportion of the steps and optionally sampling with replacement.

Usage

random_wilcox_walk(
  .num_walks = 25,
  .n = 100,
  .m = 10,
  .k = 10,
  .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. (Maps to nn in rwilcox())

.m

Number of observations in the first sample for Wilcoxon. Default is 10.

.k

Number of observations in the second sample for Wilcoxon. Default is 10.

.initial_value

A numeric value indicating the initial value of the walks. Default is 0.

.samp

A logical value indicating whether to sample the Wilcoxon 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.

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:

• walk_number: Factor representing the walk number.

• x: Step index.

• y: Wilcoxon distribution values.

• cum_sum: Cumulative sum of y.

• cum_prod: Cumulative product of y.

• cum_min: Cumulative minimum of y.

• cum_max: Cumulative maximum of y.

The tibble includes attributes for the function parameters.

See also

Other Generator Functions: brownian_motion(), discrete_walk(), geometric_brownian_motion(), random_normal_drift_walk(), random_normal_walk(), random_smirnov_walk(), random_t_walk(), random_uniform_walk(), random_weibull_walk()

Other Discrete Distribution: discrete_walk(), random_smirnov_walk()

Author

Steven P. Sanderson II, MPH

Examples

set.seed(123)
random_wilcox_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 1                     1    35        35          0        35        35
#>  2 1                     2    26        61          0        26        35
#>  3 1                     3    74       135          0        26        74
#>  4 1                     4    59       194          0        26        74
#>  5 1                     5    46       240          0        26        74
#>  6 1                     6    38       278          0        26        74
#>  7 1                     7    53       331          0        26        74
#>  8 1                     8    54       385          0        26        74
#>  9 1                     9    19       404          0        19        74
#> 10 1                    10    55       459          0        19        74
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>

set.seed(123)
random_wilcox_walk(.dimensions = 2) |>
  head() |>
  t()
#>             [,1]       [,2]       [,3]       [,4]       [,5]       [,6]      
#> walk_number "1"        "1"        "1"        "1"        "1"        "1"       
#> step_number "1"        "2"        "3"        "4"        "5"        "6"       
#> x           "35"       "26"       "74"       "59"       "46"       "38"      
#> y           "50"       "39"       "54"       "30"       "51"       "51"      
#> cum_sum_x   " 35"      " 61"      "135"      "194"      "240"      "278"     
#> cum_sum_y   " 50"      " 89"      "143"      "173"      "224"      "275"     
#> cum_prod_x  "0"        "0"        "0"        "0"        "0"        "0"       
#> cum_prod_y  "0"        "0"        "0"        "0"        "0"        "0"       
#> cum_min_x   "35"       "26"       "26"       "26"       "26"       "26"      
#> cum_min_y   "50"       "39"       "39"       "30"       "30"       "30"      
#> cum_max_x   "35"       "35"       "74"       "74"       "74"       "74"      
#> cum_max_y   "50"       "50"       "54"       "54"       "54"       "54"      
#> cum_mean_x  "35.00000" "30.50000" "45.00000" "48.50000" "48.00000" "46.33333"
#> cum_mean_y  "50.00000" "44.50000" "47.66667" "43.25000" "44.80000" "45.83333"