Generate Multiple Random Wilcoxon Signed-Rank Walks
Source:R/gen-random-wilcoxsr-walk.R
random_wilcoxon_sr_walk.RdA Wilcoxon signed-rank random walk is a stochastic process in which each step is drawn from the Wilcoxon signed-rank distribution, commonly used in nonparametric statistics. 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 sample size 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_wilcoxon_sr_walk(
.num_walks = 25,
.nn = 100,
.n = 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.
- .nn
An integer specifying the number of steps in each walk. Default is 100.
- .n
Integer or vector. Number(s) of observations in the sample(s) for rsignrank. 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.
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 ofdplyr::all_of(.dimensions).cum_prod: Cumulative product ofdplyr::all_of(.dimensions).cum_min: Cumulative minimum ofdplyr::all_of(.dimensions).cum_max: Cumulative maximum ofdplyr::all_of(.dimensions).cum_mean: Cumulative mean ofdplyr::all_of(.dimensions).
Details
The random_wilcoxon_sr_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 signed-rank distribution using
stats::rsignrank(). The user can specify the number of steps/periods (nn),
the number of samples in each walk (n), and the number of dimensions. The
function also allows for sampling a proportion of the steps and optionally
sampling with replacement.
See also
Other Generator Functions:
brownian_motion(),
discrete_walk(),
geometric_brownian_motion(),
random_hypergeometric_walk(),
random_logistic_walk(),
random_lognormal_walk(),
random_multinomial_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()
Other Discrete Distribution:
discrete_walk(),
random_hypergeometric_walk(),
random_multinomial_walk(),
random_negbinomial_walk(),
random_poisson_walk(),
random_smirnov_walk(),
random_wilcox_walk()
Examples
set.seed(123)
random_wilcoxon_sr_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 1 1 0 1 1
#> 2 1 2 0 1 0 0 1
#> 3 1 3 1 2 0 0 1
#> 4 1 4 1 3 0 0 1
#> 5 1 5 1 4 0 0 1
#> 6 1 6 1 5 0 0 1
#> 7 1 7 1 6 0 0 1
#> 8 1 8 0 6 0 0 1
#> 9 1 9 0 6 0 0 1
#> 10 1 10 0 6 0 0 1
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
random_wilcoxon_sr_walk(.dimensions = 3) |>
head() |>
t()
#> [,1] [,2] [,3] [,4] [,5]
#> walk_number "1" "1" "1" "1" "1"
#> step_number "1" "2" "3" "4" "5"
#> x "1" "0" "1" "1" "1"
#> y "0" "1" "1" "1" "0"
#> z "0" "1" "0" "0" "1"
#> cum_sum_x "1" "1" "2" "3" "4"
#> cum_sum_y "0" "1" "2" "3" "3"
#> cum_sum_z "0" "1" "1" "1" "2"
#> cum_prod_x "0" "0" "0" "0" "0"
#> cum_prod_y "0" "0" "0" "0" "0"
#> cum_prod_z "0" "0" "0" "0" "0"
#> cum_min_x "1" "0" "0" "0" "0"
#> cum_min_y "0" "0" "0" "0" "0"
#> cum_min_z "0" "0" "0" "0" "0"
#> cum_max_x "1" "1" "1" "1" "1"
#> cum_max_y "0" "1" "1" "1" "1"
#> cum_max_z "0" "1" "1" "1" "1"
#> cum_mean_x "1.0000000" "0.5000000" "0.6666667" "0.7500000" "0.8000000"
#> cum_mean_y "0.0000000" "0.5000000" "0.6666667" "0.7500000" "0.6000000"
#> cum_mean_z "0.0000000" "0.5000000" "0.3333333" "0.2500000" "0.4000000"
#> [,6]
#> walk_number "1"
#> step_number "6"
#> x "1"
#> y "0"
#> z "1"
#> cum_sum_x "5"
#> cum_sum_y "3"
#> cum_sum_z "3"
#> cum_prod_x "0"
#> cum_prod_y "0"
#> cum_prod_z "0"
#> cum_min_x "0"
#> cum_min_y "0"
#> cum_min_z "0"
#> cum_max_x "1"
#> cum_max_y "1"
#> cum_max_z "1"
#> cum_mean_x "0.8333333"
#> cum_mean_y "0.5000000"
#> cum_mean_z "0.5000000"