Generate Multiple Random Chi-Squared Walks in Multiple Dimensions

The random_chisquared_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 a chi-squared distribution. The user can specify the number of walks, the number of steps in each walk, and the parameters of the chi-squared distribution (df and ncp). The function also allows for sampling a proportion of the steps and optionally sampling with replacement.

Usage

random_chisquared_walk(
  .num_walks = 25,
  .n = 100,
  .df = 5,
  .ncp = 0,
  .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.

.df

Degrees of freedom for the chi-squared distribution. Default is 5.

.ncp

Non-centrality parameter (non-negative). Default is 0.

.initial_value

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

.samp

A logical value indicating whether to sample the chi-squared distribution 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:

• 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).

The tibble includes attributes for the function parameters.

Details

This function is a flexible generator for random walks where each step is drawn from a chi-squared distribution. The user can control the number of walks, steps per walk, degrees of freedom (df), and the non-centrality parameter (ncp). The function supports 1, 2, or 3 dimensions, and augments the output with cumulative statistics for each walk. Sampling can be performed with or without replacement, and a proportion of steps can be sampled if desired.

See also

Other Generator Functions: brownian_motion(), discrete_walk(), geometric_brownian_motion(), random_beta_walk(), random_binomial_walk(), random_cauchy_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_poisson_walk(), random_smirnov_walk(), random_t_walk(), random_uniform_walk(), random_weibull_walk(), random_wilcox_walk(), random_wilcoxon_sr_walk()

Other Continuous Distribution: brownian_motion(), geometric_brownian_motion(), random_beta_walk(), random_cauchy_walk(), random_exponential_walk(), random_f_walk(), random_gamma_walk(), random_logistic_walk(), random_lognormal_walk(), random_normal_drift_walk(), random_normal_walk(), random_t_walk(), random_uniform_walk(), random_weibull_walk()

Author

Steven P. Sanderson II, MPH

Examples

set.seed(123)
random_chisquared_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> <dbl>     <dbl>      <dbl>     <dbl>     <dbl>
#>  1 1                     1  5.08      5.08          0      5.08      5.08
#>  2 1                     2  5.49     10.6           0      5.08      5.49
#>  3 1                     3  2.74     13.3           0      2.74      5.49
#>  4 1                     4  8.02     21.3           0      2.74      8.02
#>  5 1                     5  8.21     29.5           0      2.74      8.21
#>  6 1                     6  1.22     30.8           0      1.22      8.21
#>  7 1                     7  1.22     32.0           0      1.22      8.21
#>  8 1                     8  2.25     34.2           0      1.22      8.21
#>  9 1                     9  1.29     35.5           0      1.22      8.21
#> 10 1                    10  2.42     37.9           0      1.22      8.21
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>

set.seed(123)
random_chisquared_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           "5.082440"  "5.491392"  "2.736640"  "8.018600"  "8.211414" 
#> y           " 6.251703" " 2.808596" "10.032219" " 2.673512" " 7.037088"
#> z           "4.398359"  "4.509466"  "4.602653"  "5.202429"  "2.000208" 
#> cum_sum_x   " 5.08244"  "10.57383"  "13.31047"  "21.32907"  "29.54049" 
#> cum_sum_y   " 6.251703" " 9.060299" "19.092518" "21.766030" "28.803118"
#> cum_sum_z   " 4.398359" " 8.907825" "13.510477" "18.712907" "20.713115"
#> 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   "5.082440"  "5.082440"  "2.736640"  "2.736640"  "2.736640" 
#> cum_min_y   "6.251703"  "2.808596"  "2.808596"  "2.673512"  "2.673512" 
#> cum_min_z   "4.398359"  "4.398359"  "4.398359"  "4.398359"  "2.000208" 
#> cum_max_x   "5.082440"  "5.491392"  "5.491392"  "8.018600"  "8.211414" 
#> cum_max_y   " 6.251703" " 6.251703" "10.032219" "10.032219" "10.032219"
#> cum_max_z   "4.398359"  "4.509466"  "4.602653"  "5.202429"  "5.202429" 
#> cum_mean_x  "5.082440"  "5.286916"  "4.436824"  "5.332268"  "5.908097" 
#> cum_mean_y  "6.251703"  "4.530150"  "6.364173"  "5.441508"  "5.760624" 
#> cum_mean_z  "4.398359"  "4.453912"  "4.503492"  "4.678227"  "4.142623" 
#>             [,6]       
#> walk_number "1"        
#> step_number "6"        
#> x           "1.222056" 
#> y           " 5.917235"
#> z           "2.784157" 
#> cum_sum_x   "30.76254" 
#> cum_sum_y   "34.720353"
#> cum_sum_z   "23.497272"
#> cum_prod_x  "0"        
#> cum_prod_y  "0"        
#> cum_prod_z  "0"        
#> cum_min_x   "1.222056" 
#> cum_min_y   "2.673512" 
#> cum_min_z   "2.000208" 
#> cum_max_x   "8.211414" 
#> cum_max_y   "10.032219"
#> cum_max_z   "5.202429" 
#> cum_mean_x  "5.127091" 
#> cum_mean_y  "5.786726" 
#> cum_mean_z  "3.916212"