rw30()

Quickly generate 30 random walks with 100 steps each.

Usage:

rw30()

Parameters: None

Returns: Tibble with 3,000 rows (30 walks × 100 steps)

Columns: - walk_number: Factor identifying each walk - step_number: Integer step counter (1-100) - y: Random walk values - cum_sum, cum_prod, cum_min, cum_max, cum_mean: Cumulative functions can be added but are not returned

Examples:

# Generate and view
rw30() |> head(10)
#> # A tibble: 10 × 3
#>    walk_number step_number      y
#>    <fct>             <int>  <dbl>
#>  1 1                     1  0    
#>  2 1                     2  1.05 
#>  3 1                     3  0.912
#>  4 1                     4  0.571
#>  5 1                     5  0.317
#>  6 1                     6 -0.622
#>  7 1                     7 -0.433
#>  8 1                     8  0.766
#>  9 1                     9  1.09 
#> 10 1                    10  1.33

# Visualize
rw30() |> visualize_walks()

# Analyze
rw30() |> summarize_walks(.value = y) |> head()
#> Warning: There was 1 warning in `dplyr::summarize()`.
#> ℹ In argument: `geometric_mean = exp(mean(log(y)))`.
#> Caused by warning in `log()`:
#> ! NaNs produced
#> # A tibble: 1 × 16
#>   fns   fns_name dimensions mean_val median range quantile_lo quantile_hi
#>   <chr> <chr>         <dbl>    <dbl>  <dbl> <dbl>       <dbl>       <dbl>
#> 1 rw30  Rw30              1    0.585  0.383  40.0       -11.6        13.9
#> # ℹ 8 more variables: variance <dbl>, sd <dbl>, min_val <dbl>, max_val <dbl>,
#> #   harmonic_mean <dbl>, geometric_mean <dbl>, skewness <dbl>, kurtosis <dbl>

random_normal_walk()

Generate random walks using normal distribution.

Additional Parameters: - .mu: Mean (default: 0) - .sd: Standard deviation (default: 1)

Example:

random_normal_walk(.num_walks = 10, .mu = 0, .sd = 1) |> head()
#> # A tibble: 6 × 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  1.21     1.21            0     1.21       1.21
#> 2 1                     2 -0.466    0.747           0    -0.466      1.21
#> 3 1                     3 -0.773   -0.0266          0    -0.773      1.21
#> 4 1                     4  0.929    0.902           0    -0.773      1.21
#> 5 1                     5  0.869    1.77            0    -0.773      1.21
#> 6 1                     6 -2.03    -0.262           0    -2.03       1.21
#> # ℹ 1 more variable: cum_mean_y <dbl>

random_normal_drift_walk()

Generate random walks with explicit drift component.

Additional Parameters: - .mu: Drift parameter (default: 0) - .sd: Standard deviation (default: 1)

brownian_motion()

Generate standard Brownian motion (Wiener process).

Additional Parameters: - .mu: Drift coefficient (default: 0) - .sigma: Volatility coefficient (default: 1)

geometric_brownian_motion()

Generate geometric Brownian motion (for stock prices).

Additional Parameters: - .mu: Expected return (default: 0) - .sigma: Volatility (default: 1)

Note: Initial value defaults to 100 for this function.

random_beta_walk()

Generate walks using beta distribution.

Additional Parameters: - .shape1: First shape parameter (α) - .shape2: Second shape parameter (β) - .ncp: Non-centrality parameter (default: 0)

random_cauchy_walk()

Generate walks using Cauchy distribution (heavy tails).

Additional Parameters: - .location: Location parameter (default: 0) - .scale: Scale parameter (default: 1)

random_chisquared_walk()

Generate walks using chi-squared distribution.

Additional Parameters: - .df: Degrees of freedom - .ncp: Non-centrality parameter (default: 0)

random_exponential_walk()

Generate walks using exponential distribution.

Additional Parameters: - .rate: Rate parameter (default: 1)

random_f_walk()

Generate walks using F-distribution.

Additional Parameters: - .df1: Numerator degrees of freedom - .df2: Denominator degrees of freedom - .ncp: Non-centrality parameter (default: 0)

random_gamma_walk()

Generate walks using gamma distribution.

Additional Parameters: - .shape: Shape parameter - .rate: Rate parameter (default: 1) - .scale: Scale parameter (default: 1/rate)

random_lognormal_walk()

Generate walks using log-normal distribution.

Additional Parameters: - .meanlog: Mean of log (default: 0) - .sdlog: Standard deviation of log (default: 1)

random_logistic_walk()

Generate walks using logistic distribution.

Additional Parameters: - .location: Location parameter (default: 0) - .scale: Scale parameter (default: 1)

random_t_walk()

Generate walks using Student’s t-distribution.

Additional Parameters: - .df: Degrees of freedom - .ncp: Non-centrality parameter (default: 0)

random_uniform_walk()

Generate walks using uniform distribution.

Additional Parameters: - .min: Minimum value (default: 0) - .max: Maximum value (default: 1)

random_weibull_walk()

Generate walks using Weibull distribution.

Additional Parameters: - .shape: Shape parameter - .scale: Scale parameter (default: 1)

discrete_walk()

Generate simple discrete random walks (binary up/down).

Parameters: - .num_walks: Number of walks (default: 25) - .n: Number of steps (default: 100) - .upper_bound: Maximum step size (default: 1) - .lower_bound: Minimum step size (default: -1) - .upper_probability: Probability of moving up (default: 0.5) - .initial_value: Starting value (default: 0) - .dimensions: Spatial dimensions (default: 1)

random_binomial_walk()

Generate walks using binomial distribution.

Additional Parameters: - .size: Number of trials - .prob: Probability of success (default: 0.5)

random_geometric_walk()

Generate walks using geometric distribution.

Additional Parameters: - .prob: Probability of success

random_hypergeometric_walk()

Generate walks using hypergeometric distribution.

Additional Parameters: - .m: Number of white balls - .n_param: Number of black balls - .k: Number of balls drawn

random_multinomial_walk()

Generate walks using multinomial distribution.

Additional Parameters: - .size: Number of trials - .prob: Vector of probabilities (must sum to 1)

random_negbinomial_walk()

Generate walks using negative binomial distribution.

Additional Parameters: - .size: Target number of successes - .prob: Probability of success - .mu: Alternative parameterization (mean)

random_poisson_walk()

Generate walks using Poisson distribution.

Additional Parameters: - .lambda: Rate parameter (mean and variance)

random_wilcox_walk()

Generate walks using Wilcoxon rank sum statistic distribution.

Additional Parameters: - .m: Number of observations in first group - .n_param: Number of observations in second group

random_wilcoxon_sr_walk()

Generate walks using Wilcoxon signed rank statistic distribution.

Additional Parameters: - .n_param: Number of observations

random_smirnov_walk()

Generate walks using Kolmogorov-Smirnov statistic distribution.

Additional Parameters: - .n_param: Sample size

custom_walk()

Generate random walks with custom displacement function.

Parameters: - .num_walks: Number of walks (default: 25) - .n: Number of steps (default: 100) - .displacement_fn: Custom function that returns displacement value - .initial_value: Starting value (default: 0) - .dimensions: Spatial dimensions (default: 1)

Example:

# Custom function
my_displacement <- function() {
  sample(c(-2, -1, 0, 1, 2), 1, prob = c(0.1, 0.2, 0.4, 0.2, 0.1))
}

# Generate walk
custom_walk(
  .num_walks = 10,
  .custom_fns = my_displacement
)

random_displacement_walk()

Generate walks with custom displacement from a vector.

Parameters: - .num_walks: Number of walks (default: 25) - .n: Number of steps (default: 100) - .displacement: Vector of possible displacement values - .initial_value: Starting value (default: 0) - .dimensions: Spatial dimensions (default: 1)

visualize_walks()

Create comprehensive visualizations of random walks.

Parameters: - .data: Random walk data (tibble) - .alpha: Line transparency, 0-1 (default: 0.7) - .interactive: Boolean, create interactive plot (default: FALSE) - .pluck: Select specific columns to plot (default: FALSE shows all) - Use exact plotted column names such as "y", "cum_sum_y", "cum_sum_x", or "cum_sum_z" - Short cumulative aliases such as "cum_sum" work only when they match exactly one plotted column - Can be a vector: c("y", "cum_sum_y")

Returns: - Static mode: ggplot2/patchwork object - Interactive mode: ggiraph object

Examples:

# Basic visualization
rw30() |> visualize_walks()

# Adjust transparency
rw30() |> visualize_walks(.alpha = 0.3)

# Interactive (not run in vignette)
rw30() |> visualize_walks(.interactive = TRUE)

# Select specific panels
random_normal_walk() |> visualize_walks(.pluck = "cum_sum_y")
random_normal_walk() |> visualize_walks(.pluck = c("y", "cum_sum_y", "cum_mean_y"))

summarize_walks()

Compute comprehensive summary statistics for random walks.

Parameters: - .data: Random walk data (tibble) - .value: Column name to summarize (unquoted) - .group_var: Optional grouping variable (unquoted)

Returns: Tibble with statistics: - fns: Function name - fns_name: Formatted function name - dimensions: Number of dimensions - mean_val: Mean - median: Median - range: Range (max - min) - quantile_lo, quantile_hi: Quantiles - variance, sd: Variance and standard deviation - min_val, max_val: Minimum and maximum - harmonic_mean, geometric_mean: Alternative means - skewness, kurtosis: Shape measures

Examples:

walks <- rw30()

# Overall summary
walks |> summarize_walks(.value = y) |> head()
#> Warning: There was 1 warning in `dplyr::summarize()`.
#> ℹ In argument: `geometric_mean = exp(mean(log(y)))`.
#> Caused by warning in `log()`:
#> ! NaNs produced
#> # A tibble: 1 × 16
#>   fns   fns_name dimensions mean_val median range quantile_lo quantile_hi
#>   <chr> <chr>         <dbl>    <dbl>  <dbl> <dbl>       <dbl>       <dbl>
#> 1 rw30  Rw30              1  -0.0110  0.626  40.9       -16.3        11.1
#> # ℹ 8 more variables: variance <dbl>, sd <dbl>, min_val <dbl>, max_val <dbl>,
#> #   harmonic_mean <dbl>, geometric_mean <dbl>, skewness <dbl>, kurtosis <dbl>

# By walk
walks |> 
  summarize_walks(.value = y, .group_var = walk_number) |> 
  head()
#> Warning: There were 29 warnings in `dplyr::summarize()`.
#> The first warning was:
#> ℹ In argument: `geometric_mean = exp(mean(log(y)))`.
#> ℹ In group 1: `walk_number = 1`.
#> Caused by warning in `log()`:
#> ! NaNs produced
#> ℹ Run `dplyr::last_dplyr_warnings()` to see the 28 remaining warnings.
#> # A tibble: 6 × 17
#>   walk_number fns   fns_name dimensions mean_val median range quantile_lo
#>   <fct>       <chr> <chr>         <dbl>    <dbl>  <dbl> <dbl>       <dbl>
#> 1 1           rw30  Rw30              1     4.91   5.21 15.5       -2.24 
#> 2 2           rw30  Rw30              1    -6.53  -7.71 16.8      -14.4  
#> 3 3           rw30  Rw30              1     2.55   2.72 11.9       -2.69 
#> 4 4           rw30  Rw30              1     3.84   4.13  8.64      -0.260
#> 5 5           rw30  Rw30              1    -2.98  -2.53 15.5       -9.07 
#> 6 6           rw30  Rw30              1    -3.51  -3.32 17.5      -11.5  
#> # ℹ 9 more variables: quantile_hi <dbl>, variance <dbl>, sd <dbl>,
#> #   min_val <dbl>, max_val <dbl>, harmonic_mean <dbl>, geometric_mean <dbl>,
#> #   skewness <dbl>, kurtosis <dbl>

# Cumulative sum
walks |>
  dplyr::mutate(cum_sum = cumsum(y)) |>
  summarize_walks(.value = cum_sum) |>
  head()
#> Warning: There was 1 warning in `dplyr::summarize()`.
#> ℹ In argument: `geometric_mean = exp(mean(log(cum_sum)))`.
#> Caused by warning in `log()`:
#> ! NaNs produced
#> # A tibble: 1 × 16
#>   fns   fns_name dimensions mean_val median range quantile_lo quantile_hi
#>   <chr> <chr>         <dbl>    <dbl>  <dbl> <dbl>       <dbl>       <dbl>
#> 1 rw30  Rw30              1     258.   276. 2988.      -1256.       1482.
#> # ℹ 8 more variables: variance <dbl>, sd <dbl>, min_val <dbl>, max_val <dbl>,
#> #   harmonic_mean <dbl>, geometric_mean <dbl>, skewness <dbl>, kurtosis <dbl>

subset_walks()

Extract walks with extreme values.

Parameters: - .data: Random walk data (tibble) - .value: Column name to subset by (default: “y”) - .type: Type of subset (“max”, “min”, or “both”)

Returns: Tibble containing only the selected walk

Examples:

# Walk with maximum value
walks |> subset_walks(.type = "max", .value = "y")

# Walk with minimum value
walks |> subset_walks(.type = "min", .value = "y")

confidence_interval()

Calculate confidence interval for a vector.

Parameters: - .x: Numeric vector - .interval: Confidence level (default: 0.95 for 95% CI)

Returns: Tibble with columns: - lower: Lower confidence bound - upper: Upper confidence bound

Example:

x <- rnorm(1000, mean = 10, sd = 2)
confidence_interval(x)

# 99% CI
confidence_interval(x, .interval = 0.99)

running_quantile()

Calculate running quantile at each position.

Parameters: - .x: Numeric vector - .probs: Probability value (0-1) - .window: Window size (positive integer; number of points to include in each running quantile calculation)

Returns: Numeric vector of same length

Example:

x <- rnorm(100)
running_quantile(x, .probs = 0.5, .window = 5)  # Running median

euclidean_distance()

Calculate Euclidean distance from origin for multi-dimensional walks.

Parameters: - .data: Multi-dimensional random walk data (tibble)

Returns: Original data with added distance column

Example:

walk_2d <- random_normal_walk(.dimensions = 2)
walk_2d |> euclidean_distance(.x = x, .y = y)

Cumulative Functions

These are automatically included in walk data:

• std_cum_sum_augment(): Cumulative sum
• std_cum_prod_augment(): Cumulative product
• std_cum_min_augment(): Cumulative minimum
• std_cum_max_augment(): Cumulative maximum
• std_cum_mean_augment(): Cumulative mean

Generally used internally, but can be applied to custom data.

rand_walk_helper()

Internal helper for adding cumulative columns.

Parameters: - .data: Data frame - .value: Initial value

Returns: Data frame with cumulative columns added

Note: Typically used internally by generator functions.

convert_snake_to_title_case()

Convert snake_case strings to Title Case.

Parameters: - string: Character string in snake_case

Returns: Character string in Title Case

Example:

convert_snake_to_title_case("random_normal_walk")
#> "Random Normal Walk"

convert_snake_to_title_case("cum_sum")
#> "Cumulative Sum"

get_attributes()

Get attributes without row names.

Parameters: - .data: Object with attributes

Returns: List of attributes (excluding row.names)

Example:

walks <- rw30()
get_attributes(walks)
#> $names
#> [1] "walk_number" "step_number" "y"          
#> 
#> $class
#> [1] "tbl_df"     "tbl"        "data.frame"
#> 
#> $num_walks
#> [1] 30
#> 
#> $num_steps
#> [1] 100
#> 
#> $mu
#> [1] 0
#> 
#> $sd
#> [1] 1
#> 
#> $fns
#> [1] "rw30"
#> 
#> $dimension
#> [1] 1

Return Format

All generator functions return a tibble with consistent structure:

1D Walks:

# A tibble: N × 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>
  # ... with 1 more column: cum_mean_y

2D Walks:

# A tibble: N × 14
  walk_number step_number     x     y cum_sum_x cum_sum_y cum_prod_x cum_prod_y
  <fct>             <int> <dbl> <dbl>     <dbl>     <dbl>      <dbl>      <dbl>
  # ... with 6 more columns: cum_min_x, cum_min_y, cum_max_x, cum_max_y,
  #   cum_mean_x, cum_mean_y

3D Walks:

# A tibble: N × 20
  walk_number step_number     x     y     z cum_sum_x cum_sum_y cum_sum_z
  <fct>             <int> <dbl> <dbl> <dbl>     <dbl>     <dbl>     <dbl>
  # ... with 12 more columns for cumulative functions

Attributes

All generated walks include attributes:

walks <- random_normal_walk(.num_walks = 10, .n = 100)
atb <- attributes(walks)
atb[!names(atb) %in% c("row.names")]
#> $names
#> [1] "walk_number" "step_number" "y"           "cum_sum_y"   "cum_prod_y" 
#> [6] "cum_min_y"   "cum_max_y"   "cum_mean_y" 
#> 
#> $class
#> [1] "tbl_df"     "tbl"        "data.frame"
#> 
#> $n
#> [1] 100
#> 
#> $num_walks
#> [1] 10
#> 
#> $mu
#> [1] 0
#> 
#> $sd
#> [1] 0.1
#> 
#> $initial_value
#> [1] 0
#> 
#> $replace
#> [1] TRUE
#> 
#> $samp
#> [1] TRUE
#> 
#> $samp_size
#> [1] 80
#> 
#> $periods
#> [1] 80
#> 
#> $fns
#> [1] "random_normal_walk"
#> 
#> $dimensions
#> [1] 1

By Category

Generation: - rw30() - Quick 30 walks - random_normal_walk() - Normal distribution - brownian_motion() - Brownian motion - geometric_brownian_motion() - GBM - discrete_walk() - Binary walk - 20+ more distribution generators

Visualization: - visualize_walks() - Main plotting function

Analysis: - summarize_walks() - Summary statistics - subset_walks() - Extract extremes - euclidean_distance() - Distance calculations - confidence_interval() - Confidence intervals - running_quantile() - Running quantiles

Utilities: - rand_walk_helper() - Add cumulative columns - convert_snake_to_title_case() - String formatting - get_attributes() - Get attributes