RandomWalker API Reference

API Reference

Complete reference for all RandomWalker functions, organized by category.

Automatic Random Walks
Continuous Distribution Generators
Discrete Distribution Generators
Custom Walks
Visualization Functions
Statistical Functions
Vector Functions
Utility Functions

Automatic Random Walks

`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 -1.40
#>  3 1                     3 -1.14
#>  4 1                     4 -3.58
#>  5 1                     5 -3.59
#>  6 1                     6 -2.97
#>  7 1                     7 -1.82
#>  8 1                     8 -3.64
#>  9 1                     9 -3.89
#> 10 1                    10 -4.13

# Visualize
rw30() |> visualize_walks()

Visualize 30 random walks

# Analyze
rw30() |> summarize_walks(.value = y) |> head()
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
#> 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    0.467  0.355  47.2       -12.7        12.6
#> # ℹ 8 more variables: variance <dbl>, sd <dbl>, min_val <dbl>, max_val <dbl>,
#> #   harmonic_mean <dbl>, geometric_mean <dbl>, skewness <dbl>, kurtosis <dbl>

Continuous Distribution Generators

All continuous distribution generators share these common parameters:

Parameter	Type	Default	Description
`.num_walks`	Integer	25	Number of walks to generate
`.n`	Integer	100	Number of steps per walk
`.initial_value`	Numeric	0	Starting value
`.dimensions`	Integer	1	Spatial dimensions (1, 2, or 3)

`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 -0.342    -0.342          0    -0.342    -0.342
#> 2 1                     2  0.169    -0.173          0    -0.342     0.169
#> 3 1                     3 -0.804    -0.977          0    -0.804     0.169
#> 4 1                     4 -0.876    -1.85           0    -0.876     0.169
#> 5 1                     5  2.08      0.229          0    -0.876     2.08 
#> 6 1                     6  2.20      2.42           0    -0.876     2.20 
#> # 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 Distribution Generators

`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 Walks

`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)

Visualization Functions

`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 attributes to plot (default: FALSE shows all) - Options: "y", "cum_sum", "cum_prod", "cum_min", "cum_max", "cum_mean" - Can be a vector: c("y", "cum_sum")

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

Examples:

# Basic visualization
rw30() |> visualize_walks()

Basic visualization of random walks

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

Random walks with adjusted transparency

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

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

Statistical Functions

`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   -0.341 -0.000396  44.9       -13.1        13.1
#> # 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 28 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 27 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  -6.73   -5.81    31.6      -22.0 
#> 2 2           rw30  Rw30              1  -1.72   -2.00    14.8       -6.74
#> 3 3           rw30  Rw30              1  -7.88   -8.44    17.9      -15.5 
#> 4 4           rw30  Rw30              1   0.0631  0.0371  11.5       -4.43
#> 5 5           rw30  Rw30              1   0.837   0.0211  13.8       -4.81
#> 6 6           rw30  Rw30              1 -10.1    -9.96    15.5      -15.0 
#> # 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   -1884. -2047. 3409.      -3247.       -70.5
#> # 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")

Vector Functions

`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.

Utility Functions

`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

Data Structure

Return Format

All generator functions return a tibble with consistent structure:

1D Walks:

# A tibble: N × 8
  walk_number step_number     y cum_sum cum_prod cum_min cum_max cum_mean
  <fct>             <int> <dbl>   <dbl>    <dbl>   <dbl>   <dbl>    <dbl>

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")]
#> $class
#> [1] "tbl_df"     "tbl"        "data.frame"
#> 
#> $names
#> [1] "walk_number" "step_number" "y"           "cum_sum_y"   "cum_prod_y" 
#> [6] "cum_min_y"   "cum_max_y"   "cum_mean_y" 
#> 
#> $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

Package Information

Version: 1.0.0.9000 (development)

License: MIT

Authors: - Steven P. Sanderson II, MPH (Author, Creator, Maintainer) - Antti Rask (Contributor, Visualization)

Dependencies: - dplyr - tidyr - purrr - rlang - patchwork - NNS - ggiraph

Suggested: - knitr - rmarkdown - stats - ggplot2 - tidyselect

Function Index

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

API Reference

Quick Navigation

Automatic Random Walks

rw30()

Continuous Distribution Generators

random_normal_walk()

random_normal_drift_walk()

brownian_motion()

geometric_brownian_motion()

random_beta_walk()

random_cauchy_walk()

random_chisquared_walk()

random_exponential_walk()

random_f_walk()

random_gamma_walk()

random_lognormal_walk()

random_logistic_walk()

random_t_walk()

random_uniform_walk()

random_weibull_walk()

Discrete Distribution Generators

discrete_walk()

random_binomial_walk()

random_geometric_walk()

random_hypergeometric_walk()

random_multinomial_walk()

random_negbinomial_walk()

random_poisson_walk()

random_wilcox_walk()

random_wilcoxon_sr_walk()

random_smirnov_walk()

Custom Walks

custom_walk()

random_displacement_walk()

Visualization Functions

visualize_walks()

Statistical Functions

summarize_walks()

subset_walks()

Vector Functions

confidence_interval()

running_quantile()

euclidean_distance()

Cumulative Functions

Utility Functions

rand_walk_helper()

convert_snake_to_title_case()

get_attributes()

Data Structure

Return Format

Attributes

Package Information

Function Index

By Category

See Also

`rw30()`

`random_normal_walk()`

`random_normal_drift_walk()`

`brownian_motion()`

`geometric_brownian_motion()`

`random_beta_walk()`

`random_cauchy_walk()`

`random_chisquared_walk()`

`random_exponential_walk()`

`random_f_walk()`

`random_gamma_walk()`

`random_lognormal_walk()`

`random_logistic_walk()`

`random_t_walk()`

`random_uniform_walk()`

`random_weibull_walk()`

`discrete_walk()`

`random_binomial_walk()`

`random_geometric_walk()`

`random_hypergeometric_walk()`

`random_multinomial_walk()`

`random_negbinomial_walk()`

`random_poisson_walk()`

`random_wilcox_walk()`

`random_wilcoxon_sr_walk()`

`random_smirnov_walk()`

`custom_walk()`

`random_displacement_walk()`

`visualize_walks()`

`summarize_walks()`

`subset_walks()`

`confidence_interval()`

`running_quantile()`

`euclidean_distance()`

`rand_walk_helper()`

`convert_snake_to_title_case()`

`get_attributes()`