| Title: | Generate Random Walks Compatible with the 'tidyverse' |
| Version: | 1.0.0 |
| Description: | Generates random walks of various types by providing a set of functions that are compatible with the 'tidyverse'. The functions provided in the package make it simple to create random walks with a variety of properties, such as how many simulations to run, how many steps to take, and the distribution of random walk itself. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2.9000 |
| URL: | https://www.spsanderson.com/RandomWalker/,https://github.com/spsanderson/RandomWalker |
| BugReports: | https://github.com/spsanderson/RandomWalker/issues |
| Language: | en |
| Depends: | R (≥ 4.1.0) |
| Imports: | dplyr, tidyr, purrr, rlang, patchwork, NNS, ggiraph |
| Suggests: | knitr, rmarkdown, stats, ggplot2, tidyselect |
| VignetteBuilder: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2025-08-18 22:15:50 UTC; steve |
| Author: | Steven Sanderson [aut, cre, cph], Antti Rask [aut, cph] |
| Maintainer: | Steven Sanderson <spsanderson@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-08-18 23:50:57 UTC |
Brownian Motion
Description
Create a Brownian Motion Tibble
Usage
brownian_motion( .num_walks = 25, .n = 100, .delta_time = 1, .initial_value = 0, .dimensions = 1)Arguments
.num_walks | Total number of simulations. |
.n | Total time of the simulation. |
.delta_time | Time step size. |
.initial_value | Integer representing the initial value. |
.dimensions | The default is 1. Allowable values are 1, 2 and 3. |
Details
Brownian Motion, also known as the Wiener process, is acontinuous-time random process that describes the random movement of particlessuspended in a fluid. It is named after the physicist Robert Brown,who first described the phenomenon in 1827.
The equation for Brownian Motion can be represented as:
W(t) = W(0) + sqrt(t) * Z
Where W(t) is the Brownian motion at time t, W(0) is the initial value of theBrownian motion, sqrt(t) is the square root of time, and Z is a standardnormal random variable.
Brownian Motion has numerous applications, including modeling stock prices infinancial markets, modeling particle movement in fluids, and modeling randomwalk processes in general. It is a useful tool in probability theory andstatistical analysis.
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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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:geometric_brownian_motion(),random_beta_walk(),random_cauchy_walk(),random_chisquared_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()
Examples
set.seed(123)brownian_motion()set.seed(123)brownian_motion(.dimensions = 3) |> head() |> t()Cumulative Geometric Mean
Description
A function to return the cumulative geometric mean of a vector.
Usage
cgmean(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative geometric mean of a vector.exp(cummean(log(.x)))
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:chmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgcgmean(x)Cumulative Harmonic Mean
Description
A function to return the cumulative harmonic mean of a vector.
Usage
chmean(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative harmonic mean of a vector.1 / (cumsum(1 / .x))
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgchmean(x)Cumulative Kurtosis
Description
A function to return the cumulative kurtosis of a vector.
Usage
ckurtosis(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative kurtosis of a vector.
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),cmean(),cmedian(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgckurtosis(x)Cumulative Mean
Description
A function to return the cumulative mean of a vector.
Usage
cmean(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative mean of a vector. It usesdplyr::cummean()as the basis of the function.
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmedian(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgcmean(x)Cumulative Median
Description
A function to return the cumulative median of a vector.
Usage
cmedian(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative median of a vector.
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgcmedian(x)Confidence Interval
Description
Calculate the confidence interval
Usage
confidence_interval(.vector, .interval = 0.95)Arguments
.vector | A numeric vector of data points |
.interval | A numeric value representing the confidence level(e.g., 0.95 for 95% confidence interval) The default is 0.95 |
Details
This function calculates the confidence interval for a given vector and interval.
Value
A named vector with the lower and upper bounds of the confidence interval
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
confidence_interval(rnorm(100), 0.95)Helper function to convert a snake_case string to Title Case
Description
Converts a snake_case string to Title Case.
Usage
convert_snake_to_title_case(string)Arguments
string | A character string in snake_case format. |
Details
This function is useful for formatting strings in a more readableway, especially when dealing with variable names or identifiers that usesnake_case. This function takes a snake_case string and converts it to Title Case.It replaces underscores with spaces, capitalizes the first letter of each word,and replaces the substring "cum" with "cumulative" for better readability.
Value
A character string converted to Title Case.
Author(s)
Antti Lennart Rask
See Also
Other Utility Functions:confidence_interval(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
convert_snake_to_title_case("hello_world") # "Hello World"convert_snake_to_title_case("this_is_a_test") # "This Is A Test"convert_snake_to_title_case("cumulative_sum") # "Cumulative Sum"Cumulative Range
Description
A function to return the cumulative range of a vector.
Usage
crange(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative range of a vector. It usesmax(.x[1:k]) - min(.x[1:k]) asthe basis of the function.
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgcrange(x)Cumulative Standard Deviation
Description
A function to return the cumulative standard deviation of a vector.
Usage
csd(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative standard deviation of a vector.
Value
A numeric vector. Note: The first entry will always beNaN.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),crange(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgcsd(x)Cumulative Skewness
Description
A function to return the cumulative skewness of a vector.
Usage
cskewness(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative skewness of a vector.
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgcskewness(x)Cumulative Variance
Description
A function to return the cumulative variance of a vector.
Usage
cvar(.x)Arguments
.x | A numeric vector |
Details
A function to return the cumulative variance of a vector.exp(cummean(log(.x)))
Value
A numeric vector. Note: The first entry will always beNaN.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cskewness(),euclidean_distance(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
x <- mtcars$mpgcvar(x)Discrete Sampled Walk
Description
Thediscrete_walk function generates multiple random walks over discrete time periods.Each step in the walk is determined by a probabilistic sample from specified upper and lower bounds.This function is useful for simulating stochastic processes, such as stock price movements orother scenarios where outcomes are determined by a random process.
Usage
discrete_walk( .num_walks = 25, .n = 100, .upper_bound = 1, .lower_bound = -1, .upper_probability = 0.5, .initial_value = 100, .dimensions = 1)Arguments
.num_walks | Total number of simulations. |
.n | Total time of the simulation. |
.upper_bound | The upper bound of the random walk. |
.lower_bound | The lower bound of the random walk. |
.upper_probability | The probability of the upper bound. Default is 0.5.The lower bound is calculated as 1 - .upper_probability. |
.initial_value | The initial value of the random walk. Default is 100. |
.dimensions | The default is 1. Allowable values are 1, 2 and 3. |
Details
The functiondiscrete_walk simulates random walks for a specified number of simulations(.num_walks) over a given total time (.n). Each step in the walk is either the upperbound or the lower bound, determined by a probability (.upper_probability). The initialvalue of the walk is set by the user (.initial_value), and the cumulative sum, product,minimum, and maximum of the steps are calculated for each walk. The results are returnedin a tibble with detailed attributes, including the parameters used for the simulation.
Value
A tibble containing the generated random walks with columns dependingon 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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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 Discrete Distribution:random_binomial_walk(),random_displacement_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)discrete_walk()set.seed(123)discrete_walk(.dimensions = 3) |> head() |> t()Distance Calculations
Description
A function to calculate the Euclidean distance between two vectors.
Usage
euclidean_distance(.data, .x, .y, .pull_vector = FALSE)Arguments
.data | A data frame |
.x | A numeric vector |
.y | A numeric vector |
.pull_vector | A boolean of TRUE or FALSE. Default is FALSE which willaugment the distance to the data frame. TRUE will return a vector of the distancesas the return. |
Details
A function to calculate the Euclidean distance between two vectors. It usesthe formulasqrt((x - lag(x))^2 + (y - lag(y))^2). The function uses augmentsthe data frame with a new column calleddistance.
Value
A numeric Vector of ditances
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cskewness(),cvar(),kurtosis_vec(),rw_range(),skewness_vec()
Examples
set.seed(123)df <- rw30()euclidean_distance(df, step_number, y)euclidean_distance(df, step_number, y, TRUE) |> head(10)Helper function to generate a caption string based on provided attributes
Description
Generates a caption string based on provided attributes.
Usage
generate_caption(attributes)Arguments
attributes | A list containing various attributes that may include |
Details
This function is useful for creating descriptive captions forplots or outputs based on the attributes provided. It ensures that onlynon-null attributes are included in the caption. This function constructs acaption string by checking various attributes provided in a list.It formats the caption based on the presence of specific attributes, such asdimensions, number of steps, and statistical parameters like mu and standarddeviation (sd).
Value
A character string representing the generated caption. If noattributes are provided, it returns an empty string.
Author(s)
Antti Lennart Rask
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
attrs <- list(dimension = 3, num_steps = 100, mu = 0.5, sd = 1.2)generate_caption(attrs) # "3 dimensions, 100 steps, mu = 0.5, sd = 1.2."attrs <- list(dimension = NULL, num_steps = 50, mu = NULL, sd = 2.0)generate_caption(attrs) # "50 steps, sd = 2.0."Geometric Brownian Motion
Description
Create a Geometric Brownian Motion.
Usage
geometric_brownian_motion( .num_walks = 25, .n = 100, .mu = 0, .sigma = 0.1, .initial_value = 100, .delta_time = 0.003, .dimensions = 1)Arguments
.num_walks | Total number of simulations. |
.n | Total time of the simulation, how many |
.mu | Expected return |
.sigma | Volatility |
.initial_value | Integer representing the initial value. |
.delta_time | Time step size. |
.dimensions | The default is 1. Allowable values are 1, 2 and 3. |
Details
Geometric Brownian Motion (GBM) is a statistical method for modelingthe evolution of a given financial asset over time. It is a type of stochasticprocess, which means that it is a system that undergoes random changes overtime.
GBM is widely used in the field of finance to model the behavior of stockprices, foreign exchange rates, and other financial assets. It is based onthe assumption that the asset's price follows a random walk, meaning that itis influenced by a number of unpredictable factors such as market trends,news events, and investor sentiment.
The equation for GBM is:
dS/S = mdt + sdW
where S is the price of the asset, t is time, m is the expected return on theasset, s is the volatility of the asset, and dW is a small random change inthe asset's price.
GBM can be used to estimate the likelihood of different outcomes for a givenasset, and it is often used in conjunction with other statistical methods tomake more accurate predictions about the future performance of an asset.
This function provides the ability of simulating and estimating the parametersof a GBM process. It can be used to analyze the behavior of financialassets and to make informed investment decisions.
Value
A tibble containing the generated random walks with columns dependingon 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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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(),random_beta_walk(),random_cauchy_walk(),random_chisquared_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()
Examples
set.seed(123)geometric_brownian_motion()set.seed(123)geometric_brownian_motion(.dimensions = 3) |> head() |> t()Get Attributes
Description
Theget_attributes function takes an R object as input andreturns its attributes, omitting the row.names attribute.
Usage
get_attributes(.data)Arguments
.data | An R object from which attributes are to be extracted. |
Details
This function retrieves the attributes of a given R object,excluding the row.names attribute.
Value
A list of attributes of the input R object, excluding row.names.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
get_attributes(rw30())get_attributes(iris)get_attributes(mtcars)Compute Kurtosis of a Vector
Description
This function takes in a vector as it's input and will return the kurtosisof that vector. The length of this vector must be at least four numbers. Thekurtosis explains the sharpness of the peak of a distribution of data.
((1/n) * sum(x - mu})^4) / ((()1/n) * sum(x - mu)^2)^2
Usage
kurtosis_vec(.x)Arguments
.x | A numeric vector of length four or more. |
Details
A function to return the kurtosis of a vector.
Value
The kurtosis of a vector
Author(s)
Steven P. Sanderson II, MPH
See Also
https://en.wikipedia.org/wiki/Kurtosis
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),rw_range(),skewness_vec()
Examples
set.seed(123)kurtosis_vec(rnorm(100, 3, 2))Get Column Names
Description
This function generates the column names of a rand walkdata frame.
Usage
rand_walk_column_names(.rand_data, .dim_names, .num_sims, .t)Arguments
.rand_data | A data frame from which column names are to be extracted. |
.dim_names | The dimnames passed from the rand walk function. |
.num_sims | The number of simulations. |
.t | Ther periods in the walk |
Details
Therand_walk_column_names function takes a data frame as input andreturns the rand walk data with column names.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Random Walk Helper
Description
A function to help build random walks by mutating a data frame.
Usage
rand_walk_helper(.data, .value)Arguments
.data | The data frame to mutate. |
.value | The .initial_value to use. This is passed from the random walkfunction being called by the end user. |
Details
A function to help build random walks by mutating a data frame. This mutationadds the following columns to the data frame:cum_sum,cum_prod,cum_min,cum_max, andcum_mean. The function is used internally by certain functionsthat generate random walks.
Value
A modified data frame/tibble with the following columns added:
cum_sum: Cumulative sum ofy.cum_prod: Cumulative product ofy.cum_min: Cumulative minimum ofy.cum_max: Cumulative maximum ofy.cum_mean: Cumulative mean ofy.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
df <- data.frame( walk_number = factor(rep(1L:25L, each = 30L)), x = rep(1L:30L, 25L), y = rnorm(750L, 0L, 1L) )rand_walk_helper(df, 100)Generate Multiple Random Beta Walks in Multiple Dimensions
Description
Therandom_beta_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 Beta distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the Beta distribution (shape1, shape2, ncp). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_beta_walk( .num_walks = 25, .n = 100, .shape1 = 2, .shape2 = 2, .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. Must be >= 1. Default is 100. |
.shape1 | Non-negative parameter of the Beta distribution. Default is 2. |
.shape2 | Non-negative parameter of the Beta distribution. Default is 2. |
.ncp | Non-centrality parameter (ncp >= 0). 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 Beta 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
Theshape1,shape2, andncp parameters can be single values or vectors of length equal to the number of dimensions. If vectors are provided, each dimension uses its corresponding value.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_cauchy_walk(),random_chisquared_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()
Examples
set.seed(123)random_beta_walk()set.seed(123)random_beta_walk(.dimensions = 3, .shape1 = c(2, 3, 4), .shape2 = c(2, 3, 4), .ncp = c(0, 1, 2)) |> head() |> t()Generate Multiple Random Binomial Walks in Multiple Dimensions
Description
Therandom_binomial_walk function generates multiple random walks using the binomial distribution viarbinom().The user can specify the number of walks, the number of steps in each walk, the number of trials, and the probability of success.The function also allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_binomial_walk( .num_walks = 25, .n = 100, .size = 10, .prob = 0.5, .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 observations per walk. Must be greater than 0. Default is 100. |
.size | An integer specifying the number of trials (zero or more). Default is 10. |
.prob | A numeric value specifying the probability of success on each trial. Must be 0 <= .prob <= 1. Default is 0.5. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the binomial 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function generates random walks where each step is drawn from the binomial distribution usingrbinom().The user can control the number of walks, steps per walk, the number of trials (size), and the probability of success (prob).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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_cauchy_walk(),random_chisquared_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 Discrete Distribution:discrete_walk(),random_displacement_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_binomial_walk()set.seed(123)random_binomial_walk(.dimensions = 2) |> head() |> t()Generate Multiple Random Cauchy Walks in Multiple Dimensions
Description
Therandom_cauchy_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 Cauchy distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the Cauchy distribution (location and scale). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_cauchy_walk( .num_walks = 25, .n = 100, .location = 0, .scale = 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. |
.n | An integer specifying the number of steps in each walk. Default is 100. |
.location | A numeric value indicating the location parameter of the Cauchy distribution. Default is 0. |
.scale | A numeric value indicating the scale parameter of the Cauchy distribution. Default is 1. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the Cauchy 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
Thelocation andscale parameters can be single values or vectors of length equal to the number of dimensions. If vectors are provided, each dimension uses its corresponding value.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_chisquared_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_chisquared_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()
Examples
set.seed(123)random_cauchy_walk()set.seed(123)random_cauchy_walk(.dimensions = 3, .location = c(0, 1, 2), .scale = c(1, 2, 3)) |> head() |> t()Generate Multiple Random Chi-Squared Walks in Multiple Dimensions
Description
Therandom_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 theparameters of the chi-squared distribution (df and ncp). The functionalso 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
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()
Examples
set.seed(123)random_chisquared_walk()set.seed(123)random_chisquared_walk(.dimensions = 3) |> head() |> t()Generate a Random Displacement Walk in 2D
Description
Therandom_displacement_walk function generates a single random walk in 2 dimensions (x, y),where each step is a random displacement in both x and y directions, sampled from the provideddisplacement and distance spaces. The walk disregards steps where both x and y displacements are zero.
Usage
random_displacement_walk( .num_walks = 25, .seed = NULL, .n = 100, .distance_space = c(0, 1, 2, 3, 4), .displacement = c(-1, 1), .dimensions = 1)Arguments
.num_walks | An integer specifying the number of random walks to generate. Default is 25. |
.seed | An optional value to set the random seed. If NULL, no seed is set. Default is NULL. |
.n | The number of steps in the walk. Must be >= 0. Default is 100. |
.distance_space | A numeric vector of possible step distances. Default is c(0, 1, 2, 3, 4). |
.displacement | A numeric vector of possible step directions. Default is c(-1, 1). |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Value
A tibble with columns depending on the number of dimensions:
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 tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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 Discrete Distribution:discrete_walk(),random_binomial_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
random_displacement_walk(.n = 10, .seed = Sys.Date())Generate Multiple Random Exponential Walks in Multiple Dimensions
Description
Therandom_exponential_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 an exponential distribution.
Usage
random_exponential_walk( .num_walks = 25, .n = 100, .rate = 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. |
.n | An integer specifying the number of steps in each walk. Must be >= 1. Default is 100. |
.rate | A numeric value or vector indicating the rate parameter(s) of the exponential distribution. Default is 1. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the exponential 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
Therate parameter can be a single value or a vector of length equal to the number of dimensions. If a vector is provided, each dimension uses its corresponding rate.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_walk(),random_displacement_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_chisquared_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()
Examples
set.seed(123)random_exponential_walk()set.seed(123)random_exponential_walk(.dimensions = 3, .rate = c(0.1, 0.1, 0.2)) |> head() |> t()Generate Multiple Random F Walks in Multiple Dimensions
Description
Therandom_f_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 an F distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the F distribution (df1, df2, ncp). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_f_walk( .num_walks = 25, .n = 100, .df1 = 5, .df2 = 5, .ncp = NULL, .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. |
.df1 | Degrees of freedom 1 for the F distribution. Default is 5. |
.df2 | Degrees of freedom 2 for the F distribution. Default is 5. |
.ncp | Non-centrality parameter. Default is NULL (central F). |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the F 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function is a flexible generator for random walks where each step is drawn from an F distribution.The user can control the number of walks, steps per walk, degrees of freedom (df1, df2), and optionally the non-centrality parameter (ncp).If.ncp is left as NULL, the function generates F values using the ratio of chi-squared distributions as described in base R documentation.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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_walk(),random_displacement_walk(),random_exponential_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_chisquared_walk(),random_exponential_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()
Examples
set.seed(123)random_f_walk()set.seed(123)random_f_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Gamma Walks in Multiple Dimensions
Description
Therandom_gamma_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 gamma distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the gamma distribution (shape, scale, rate). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_gamma_walk( .num_walks = 25, .n = 100, .shape = 1, .scale = 1, .rate = NULL, .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. Must be greater than 0. Default is 100. |
.shape | A positive numeric value for the shape parameter. Default is 1. |
.scale | A positive numeric value for the scale parameter. Default is 1. |
.rate | A positive numeric value for the rate parameter. Default is NULL (ignored if scale is provided). |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the gamma 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function is a flexible generator for random walks where each step is drawn from a gamma distribution.The user can control the number of walks, steps per walk, and the shape, scale, and rate parameters for the distribution.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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_walk(),random_displacement_walk(),random_exponential_walk(),random_f_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_chisquared_walk(),random_exponential_walk(),random_f_walk(),random_logistic_walk(),random_lognormal_walk(),random_normal_drift_walk(),random_normal_walk(),random_t_walk(),random_uniform_walk(),random_weibull_walk()
Examples
set.seed(123)random_gamma_walk()set.seed(123)random_gamma_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Geometric Walks in Multiple Dimensions
Description
Therandom_geometric_walk function generates multiple random walks using the geometric distribution viargeom().The user can specify the number of walks, the number of steps in each walk, and the probability of success in each trial.The function also allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_geometric_walk( .num_walks = 25, .n = 100, .prob = 0.5, .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 observations per walk. Default is 100. |
.prob | A numeric value specifying the probability of success in each trial. Must be 0 < .prob <= 1. Default is 0.5. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the geometric 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function generates random walks where each step is drawn from the geometric distribution usingrgeom().The user can control the number of walks, steps per walk, and the probability of success (prob).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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_walk(),random_displacement_walk(),random_exponential_walk(),random_f_walk(),random_gamma_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 Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_geometric_walk()set.seed(123)random_geometric_walk(.dimensions = 2) |> head() |> t()Generate Multiple Random Hypergeometric Walks in Multiple Dimensions
Description
Therandom_hypergeometric_walk function generates multiple random walks using the hypergeometric distribution viarhyper().The user can specify the number of walks, the number of steps in each walk, and the urn parameters (m, n, k).The function also allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_hypergeometric_walk( .num_walks = 25, .nn = 100, .m = 50, .n = 50, .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. |
.nn | An integer specifying the number of observations per walk. Default is 100. |
.m | An integer specifying the number of white balls in the urn. Default is 50. |
.n | An integer specifying the number of black balls in the urn. Default is 50. |
.k | An integer specifying the number of balls drawn from the urn. 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 hypergeometric 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function generates random walks where each step is drawn from the hypergeometric distribution usingrhyper().The user can control the number of walks, steps per walk, and the urn parameters: m (white balls), n (black balls), and k (balls drawn).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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_walk(),random_displacement_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_geometric_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 Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_geometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_hypergeometric_walk()set.seed(123)random_hypergeometric_walk(.dimensions = 2) |> head() |> t()Generate Multiple Random Logistic Walks in Multiple Dimensions
Description
Therandom_logistic_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 logistic distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the logistic distribution (location and scale). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_logistic_walk( .num_walks = 25, .n = 100, .location = 0, .scale = 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. |
.n | An integer specifying the number of steps in each walk. Default is 100. |
.location | A numeric value indicating the location parameter of the logistic distribution. Default is 0. |
.scale | A numeric value indicating the scale parameter of the logistic distribution. Default is 1. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the logistic 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function is a flexible generator for random walks where each step is drawn from a logistic distribution.The user can control the number of walks, steps per walk, and the location and scale parameters for the distribution.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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_walk(),random_displacement_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_geometric_walk(),random_hypergeometric_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_chisquared_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_lognormal_walk(),random_normal_drift_walk(),random_normal_walk(),random_t_walk(),random_uniform_walk(),random_weibull_walk()
Examples
set.seed(123)random_logistic_walk()set.seed(123)random_logistic_walk(.dimensions = 2) |> head() |> t()Generate Multiple Random Lognormal Walks in Multiple Dimensions
Description
Therandom_lognormal_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 lognormal distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the lognormal distribution (meanlog and sdlog). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_lognormal_walk( .num_walks = 25, .n = 100, .meanlog = 0, .sdlog = 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. |
.n | An integer specifying the number of steps in each walk. Default is 100. |
.meanlog | A numeric value indicating the meanlog parameter of the lognormal distribution. Default is 0. |
.sdlog | A numeric value indicating the sdlog parameter of the lognormal distribution. Default is 1. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the lognormal 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function is a flexible generator for random walks where each step is drawn from a lognormal distribution.The user can control the number of walks, steps per walk, and the meanlog and sdlog parameters for the distribution.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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_walk(),random_displacement_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_logistic_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_chisquared_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_logistic_walk(),random_normal_drift_walk(),random_normal_walk(),random_t_walk(),random_uniform_walk(),random_weibull_walk()
Examples
set.seed(123)random_lognormal_walk()set.seed(123)random_lognormal_walk(.dimensions = 2) |> head() |> t()Generate Multiple Random Multinomial Walks
Description
A multinomial random walk is a stochastic process in which each step is drawnfrom the multinomial distribution. This function allows for the simulation ofmultiple independent random walks in one, two, or three dimensions, with usercontrol over the number of walks, steps, trials, probabilities, and dimensions.Sampling options allow for further customization, including the ability tosample a proportion of steps and to sample with or without replacement. Theresulting data frame includes cumulative statistics for each walk.
Usage
random_multinomial_walk( .num_walks = 25, .n = 100, .size = 3, .prob = rep(1/3, .n), .initial_value = 0, .samp = TRUE, .replace = TRUE, .sample_size = 0.8, .dimensions = 1)Arguments
.num_walks | Integer. Number of random walks to generate. Default is 25. |
.n | Integer. Length of each walk (number of steps). Default is 100. |
.size | Integer. Number of trials for each multinomial draw. Default is 3. |
.prob | Numeric vector. Probabilities for each outcome. Default is rep(1/3, .n). |
.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. |
Details
Therandom_multinomial_walk function generates multiple random walks usingthe multinomial distribution viastats::rmultinom(). Each walk is a sequenceof steps where each step is a random draw from the multinomial distribution.The user can specify the number of walks, steps, trials per step, and theprobability vector. Sampling options allow for further customization,including the ability to sample a proportion of steps and to sample with orwithout replacement. The resulting data frame includes cumulative statisticsfor each walk, making it suitable for simulation studies and visualization.
Value
A tibble containing the generated random walks with columns:
walk_number: Factor representing the walk number.step_number: Step index.value: Value of the walk at each step.Cumulative statistics: cum_sum, cum_prod, cum_min, cum_max, cum_mean.
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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_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 Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_negbinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_multinomial_walk()set.seed(123)random_multinomial_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Negative Binomial Walks
Description
A Negative Binomial random walk is a stochastic process in which each step isdrawn from the Negative Binomial distribution, commonly used for modeling countdata with overdispersion. This function allows for the simulation of multipleindependent random walks in one, two, or three dimensions, with user control overthe number of walks, steps, and the distribution parameters. Sampling optionsallow for further customization, including the ability to sample a proportion ofsteps and to sample with or without replacement. The resulting data frame includescumulative statistics for each walk, making it suitable for simulation studies andvisualization.
Usage
random_negbinomial_walk( .num_walks = 25, .n = 100, .size = 1, .prob = 0.5, .mu = NULL, .initial_value = 0, .samp = TRUE, .replace = TRUE, .sample_size = 0.8, .dimensions = 1)Arguments
.num_walks | An integer specifying the number of random walks togenerate. Default is 25. |
.n | Integer. Number of random variables to return for each walk. Default is 100. |
.size | Integer. Number of successful trials or dispersion parameter. Default is 1.This must also match the number of dimensions, for example if |
.prob | Numeric. Probability of success in each trial (0 < prob <= 1). Default is 0.5.This must also match the number of dimensions, for example if |
.mu | Numeric. Alternative parametrization via mean. Default is NULL.This must also match the number of dimensions, for example if |
.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. |
Details
Therandom_negbinomial_walk function generates multiple random walks in1, 2, or 3 dimensions. Each walk is a sequence of steps where each step isa random draw from the Negative Binomial distribution usingstats::rnbinom().The user can specify the number of samples in each walk (n), the size parameter,the probability of success (prob), and/or the mean (mu), and the number ofdimensions. The function also allows for sampling a proportion of the steps andoptionally sampling with replacement.
Value
A tibble containing the generated random walks with columns dependingon 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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_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 Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_negbinomial_walk()set.seed(123)random_negbinomial_walk(.dimensions = 3, .size = c(1,2,3), .prob = c(0.5,0.7,0.9) ) |> head() |> t()Generate Multiple Random Walks with Drift
Description
This function generates a specified number of random walks, each consistingof a specified number of steps. The steps are generated from a normaldistribution with a given mean and standard deviation. An additional driftterm is added to each step to introduce a consistent directional componentto the walks.
Usage
random_normal_drift_walk( .num_walks = 25, .n = 100, .mu = 0, .sd = 1, .drift = 0.1, .initial_value = 0, .dimensions = 1)Arguments
.num_walks | Integer. The number of random walks to generate. Default is 25. |
.n | Integer. The number of steps in each random walk. Default is 100. |
.mu | Numeric. The mean of the normal distribution used for generating steps. Default is 0. |
.sd | Numeric. The standard deviation of the normal distribution used for generating steps. Default is 1. |
.drift | Numeric. The drift term to be added to each step. Default is 0.1. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.dimensions | The default is 1. Allowable values are 1, 2 and 3. |
Details
This function generates multiple random walks with a specified drift.Each walk is generated using a normal distribution for the steps, with anadditional drift term added to each step.
Value
A tibble containing the generated random walks with columns dependingon 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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_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_chisquared_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_logistic_walk(),random_lognormal_walk(),random_normal_walk(),random_t_walk(),random_uniform_walk(),random_weibull_walk()
Examples
set.seed(123)random_normal_drift_walk()set.seed(123)random_normal_drift_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Normal Walks in Multiple Dimensions
Description
Therandom_normal_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 normal distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the normal distribution (mean and standard deviation). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_normal_walk( .num_walks = 25, .n = 100, .mu = 0, .sd = 0.1, .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. |
.n | An integer specifying the number of steps in each walk. Default is 100. |
.mu | A numeric value indicating the mean of the normal distribution. Default is 0. |
.sd | A numeric value indicating the standard deviation of the normal distribution. Default is 0.1. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the normal 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 |
.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 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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_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_chisquared_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_logistic_walk(),random_lognormal_walk(),random_normal_drift_walk(),random_t_walk(),random_uniform_walk(),random_weibull_walk()
Examples
set.seed(123)random_normal_walk()set.seed(123)random_normal_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Poisson Walks
Description
A Poisson random walk is a stochastic process in which each step is drawn fromthe Poisson distribution, commonly used for modeling count data. This functionallows for the simulation of multiple independent random walks in one, two, orthree dimensions, with user control over the number of walks, steps, and thelambda parameter for the distribution. Sampling options allow for furthercustomization, including the ability to sample a proportion of steps and tosample with or without replacement. The resulting data frame includes cumulativestatistics for each walk, making it suitable for simulation studies andvisualization.
Usage
random_poisson_walk( .num_walks = 25, .n = 100, .lambda = 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 togenerate. Default is 25. |
.n | Integer. Number of random variables to return for each walk. Default is 100. |
.lambda | Numeric or vector. Mean(s) for the Poisson distribution. 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). Defaultis 0.8. |
.dimensions | Integer. Number of dimensions (1, 2, or 3). Default is1. |
Details
Therandom_poisson_walk function generates multiple random walks in1, 2, or 3 dimensions. Each walk is a sequence of steps where each step isa random draw from the Poisson distribution usingbase::rpois(). The usercan specify the number of samples in each walk (n), the lambda parameter forthe Poisson distribution, and the number of dimensions. The function also allowsfor sampling a proportion of the steps and optionally sampling with replacement.
Value
A tibble containing the generated random walks with columns dependingon 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 intwo dimensions.x,y,z: If.dimensions = 3, the values of the walkin 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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_smirnov_walk(),random_t_walk(),random_uniform_walk(),random_weibull_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Other Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_smirnov_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_poisson_walk()set.seed(123)random_poisson_walk(.dimensions = 3, .lambda = c(1, 2, 3)) |> head() |> t()Generate Multiple Random Smirnov Walks in Multiple Dimensions
Description
Therandom_smirnov_walk function generates multiple random walks using the Smirnov distribution viarsmirnov().The user can specify the number of walks, the number of steps in each walk, the sizes parameter, and the alternative hypothesis.The function also allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_smirnov_walk( .num_walks = 25, .n = 100, .sizes = c(1, 1), .z = NULL, .alternative = "two.sided", .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. |
.sizes | A numeric vector of length 2 specifying the sizes parameter for rsmirnov. Default is c(1, 1). |
.z | Optional numeric vector for the z parameter in rsmirnov. Default is NULL. |
.alternative | One of "two.sided" (default), "less", or "greater". Indicates the type of test statistic. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the Smirnov 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function generates random walks where each step is drawn from the Smirnov distribution usingrsmirnov().The user can control the number of walks, steps per walk, thesizes parameter (defaultc(1, 1)), and thealternative hypothesis.The parameterz can be provided or left asNULL (default). 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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_t_walk(),random_uniform_walk(),random_weibull_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Other Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_poisson_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_smirnov_walk()set.seed(123)random_smirnov_walk(.dimensions = 2) |> head() |> t()Generate Multiple Random t-Distributed Walks in Multiple Dimensions
Description
Therandom_t_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 t-distribution.The user can specify the number of walks, the number of steps in each walk, and thedegrees of freedom for the t-distribution. The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_t_walk( .num_walks = 25, .n = 100, .df = 5, .initial_value = 0, .ncp = 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 t-distribution. Default is 5. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.ncp | A numeric value for the non-centrality parameter for the t-distribution. Default is 0. |
.samp | A logical value indicating whether to sample the t-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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function is a flexible generator for random walks where each step is drawn from a t-distribution.The user can control the number of walks, steps per walk, degrees of freedom, and optionally the non-centrality parameter (ncp).If.ncp is left blank, the function uses the default behavior ofrt() from base R, which setsncp = 0.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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_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_chisquared_walk(),random_exponential_walk(),random_f_walk(),random_gamma_walk(),random_logistic_walk(),random_lognormal_walk(),random_normal_drift_walk(),random_normal_walk(),random_uniform_walk(),random_weibull_walk()
Examples
set.seed(123)random_t_walk()set.seed(123)random_t_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Uniform Walks in Multiple Dimensions
Description
Therandom_uniform_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 uniform distribution.The user can specify the number of walks, the number of steps in each walk, and theparameters of the uniform distribution (min and max). The functionalso allows for sampling a proportion of the steps and optionally sampling with replacement.
Usage
random_uniform_walk( .num_walks = 25, .n = 100, .min = 0, .max = 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. |
.n | An integer specifying the number of steps in each walk. Default is 100. |
.min | A numeric value indicating the minimum of the uniform distribution. Default is 0. |
.max | A numeric value indicating the maximum of the uniform distribution. Default is 1. |
.initial_value | A numeric value indicating the initial value of the walks. Default is 0. |
.samp | A logical value indicating whether to sample the uniform 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 |
.dimensions | An integer specifying the number of dimensions (1, 2, or 3). Default is 1. |
Details
This function is a flexible generator for random walks where each step is drawn from a uniform distribution.The user can control the number of walks, steps per walk, and the minimum and maximum values for the uniform distribution.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.
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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_weibull_walk(),random_wilcox_walk(),random_wilcoxon_sr_walk()
Other Continuous Distribution:brownian_motion(),geometric_brownian_motion(),random_beta_walk(),random_cauchy_walk(),random_chisquared_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_weibull_walk()
Examples
set.seed(123)random_uniform_walk()set.seed(123)random_uniform_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Weibull Walks in Multiple Dimensions
Description
A Weibull random walk is a stochastic process in which each step is drawnfrom the Weibull distribution, a flexible distribution commonly used to modellifetimes, reliability, and extreme values. This function allows for thesimulation of multiple independent random walks in one, two, or threedimensions, with user control over the number of walks, steps, and the shapeand scale parameters of the Weibull distribution. Sampling options allow forfurther customization, including the ability to sample a proportion of stepsand to sample with or without replacement. The resulting data frame includescumulative statistics for each walk, making it suitable for simulationstudies and visualization.
Usage
random_weibull_walk( .num_walks = 25, .n = 100, .shape = 1, .scale = 1, .initial_value = 0, .samp = TRUE, .replace = TRUE, .sample_size = 0.8, .dimensions = 1)Arguments
.num_walks | Integer. Number of walks to generate. Default is 25. |
.n | Integer. Number of steps in each walk. Default is 100. |
.shape | Numeric. Shape parameter of the Weibull distribution. Default is 1. |
.scale | Numeric. Scale parameter of the Weibull distribution. 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. |
Details
Therandom_weibull_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 theWeibull distribution usingstats::rweibull(). The user can specify thenumber of walks, the number of steps in each walk, and the parameters.shape and.scale for the Weibull distribution. The function also allowsfor sampling a proportion of the steps and optionally sampling with replacement.
Value
A data frame with the random walks and cumulative statistics as columns.
A tibble containing the generated random walks with columns dependingon 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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_wilcox_walk(),random_wilcoxon_sr_walk()
Other Continuous Distribution:brownian_motion(),geometric_brownian_motion(),random_beta_walk(),random_cauchy_walk(),random_chisquared_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()
Examples
set.seed(123)random_weibull_walk()set.seed(123)random_weibull_walk(.dimensions = 3) |> head() |> t()Generate Multiple Random Wilcoxon Walks in Multiple Dimensions
Description
Therandom_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 distributionusingstats::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 samplinga 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 |
.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 |
.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 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).
The tibble includes attributes for the function parameters.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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_wilcoxon_sr_walk()
Other Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_geometric_walk(),random_hypergeometric_walk(),random_multinomial_walk(),random_negbinomial_walk(),random_poisson_walk(),random_smirnov_walk(),random_wilcoxon_sr_walk()
Examples
set.seed(123)random_wilcox_walk()set.seed(123)random_wilcox_walk(.dimensions = 2) |> head() |> t()Generate Multiple Random Wilcoxon Signed-Rank Walks
Description
A Wilcoxon signed-rank random walk is a stochastic process in which eachstep is drawn from the Wilcoxon signed-rank distribution, commonly used innonparametric statistics. This function allows for the simulation ofmultiple independent random walks in one, two, or three dimensions, withuser control over the number of walks, steps, and the sample size parameterfor the distribution. Sampling options allow for further customization,including the ability to sample a proportion of steps and to sample with orwithout replacement. The resulting data frame includes cumulativestatistics for each walk, making it suitable for simulation studies andvisualization.
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 togenerate. 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) forrsignrank. 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). Defaultis 0.8. |
.dimensions | Integer. Number of dimensions (1, 2, or 3). Default is1. |
Details
Therandom_wilcoxon_sr_walk function generates multiple random walks in1, 2, or 3 dimensions. Each walk is a sequence of steps where each step isa random draw from the Wilcoxon signed-rank distribution usingstats::rsignrank(). The user can specify the number of steps/periods (nn),the number of samples in each walk (n), and the number of dimensions. Thefunction also allows for sampling a proportion of the steps and optionallysampling with replacement.
Value
A tibble containing the generated random walks with columns dependingon 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 intwo dimensions.x,y,z: If.dimensions = 3, the values of the walkin 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).
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:brownian_motion(),discrete_walk(),geometric_brownian_motion(),random_beta_walk(),random_binomial_walk(),random_cauchy_walk(),random_chisquared_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()
Other Discrete Distribution:discrete_walk(),random_binomial_walk(),random_displacement_walk(),random_geometric_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()set.seed(123)random_wilcoxon_sr_walk(.dimensions = 3) |> head() |> t()Running Quantile Calculation
Description
Therunning_quantile function calculates the quantile ofa vector over a sliding window, allowing for various alignment and rule options.
Usage
running_quantile( .x, .window, .probs = 0.5, .type = 7, .rule = "quantile", .align = "center")Arguments
.x | A numeric vector for which the running quantile is to be calculated. |
.window | An integer specifying the size of the sliding window. |
.probs | A numeric value between 0 and 1 indicating the desired quantileprobability (default is 0.50). |
.type | An integer from 1 to 9 specifying the quantile algorithm type(default is 7). |
.rule | A character string indicating the rule to apply at the edges ofthe window. Possible choices are:
|
.align | A character string specifying the alignment of thewindow ("center", "left", or "right"; default is "center"). |
Details
This function computes the running quantile of a numeric vector usinga specified window size and probability.
Value
A numeric vector containing the running quantile values.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
# Example usage of running_quantileset.seed(123)data <- cumsum(rnorm(50))result <- running_quantile(data, .window = 3, .probs = 0.5)print(result)plot(data, type = "l")lines(result, col = "red")Generate Random Walks
Description
Generate Random Walks
Usage
rw30()Details
The function generates random walks using the normal distribution with aspecified mean (mu) and standard deviation (sd).Each walk is generated independently and stored in a tibble. The resultingtibble is then pivoted into a long format for easier analysis.
Value
A tibble in long format with columnswalk,x, andvalue,representing the random walks. Additionally, attributesnum_walks,num_steps,mu, andsd are attached to the tibble.
Author(s)
Steven P. Sanderson II, MPH
This function generates 30 random walks with 100 steps each and pivots theresult into a long format tibble.
Examples
# Generate random walks and print the resultset.seed(123)rw30()set.seed(123)rw30() |> visualize_walks()Range
Description
A function to return the range of a vector.
Usage
rw_range(.x)Arguments
.x | A numeric vector |
Details
A function to return the range of a vector. It usesmax(.x) - min(.x) asthe basis of the function.
Value
A numeric vector
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),skewness_vec()
Examples
x <- mtcars$mpgrw_range(x)Compute Skewness of a Vector
Description
This function takes in a vector as it's input and will return the skewnessof that vector. The length of this vector must be at least four numbers. Theskewness explains the 'tailedness' of the distribution of data.
((1/n) * sum(x - mu})^3) / ((()1/n) * sum(x - mu)^2)^(3/2)
Usage
skewness_vec(.x)Arguments
.x | A numeric vector of length four or more. |
Details
A function to return the skewness of a vector.
Value
The skewness of a vector
Author(s)
Steven P. Sanderson II, MPH
See Also
https://en.wikipedia.org/wiki/Skewness
Other Vector Function:cgmean(),chmean(),ckurtosis(),cmean(),cmedian(),crange(),csd(),cskewness(),cvar(),euclidean_distance(),kurtosis_vec(),rw_range()
Examples
set.seed(123)skewness_vec(rnorm(100, 3, 2))Augment Cumulative Maximum
Description
This function augments a data frame by adding cumulative maximumcolumns for specified variables.
Usage
std_cum_max_augment(.data, .value, .names = "auto", .initial_value = 0)Arguments
.data | A data frame to augment. |
.value | A column name or names for which to compute the cumulative maximum. |
.names | Optional. A character vector of names for the new cumulativemaximum columns. Defaults to "auto", which generates names based on theoriginal column names. |
.initial_value | A numeric value to start the cumulative maximum from.Defaults to 0. |
Details
The function takes a data frame and a column name (or names) andcomputes the cumulative maximum for each specified column, starting from aninitial value. If the column names are not provided, it will throw an error.
Value
A tibble with the original data and additional columns containing thecumulative maximums.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
df <- data.frame(x = c(1, 3, 2, 5, 4), y = c(10, 7, 6, 12, 5))std_cum_max_augment(df, .value = x)std_cum_max_augment(df, .value = y, .names = c("cummax_y"))Augment Cumulative Sum
Description
This function augments a data frame by adding cumulative meancolumns for specified variables.
Usage
std_cum_mean_augment(.data, .value, .names = "auto", .initial_value = 0)Arguments
.data | A data frame to augment. |
.value | A column name or names for which to compute the cumulative mean. |
.names | Optional. A character vector of names for the new cumulativemean columns. Defaults to "auto", which generates names based on the originalcolumn names. |
.initial_value | A numeric value to start the cumulative mean from.Defaults to 0. |
Details
The function takes a data frame and a column name (or names) andcomputes the cumulative mean for each specified column, starting from aninitial value. If the column names are not provided, it will throw an error.
Value
A tibble with the original data and additional columns containing thecumulative means.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
df <- data.frame(x = c(1, 2, 3, 4, 5), y = c(10, 20, 30, 40, 50))std_cum_mean_augment(df, .value = x)std_cum_mean_augment(df, .value = y, .names = c("cummean_y"))Augment Cumulative Minimum
Description
This function augments a data frame by adding cumulative minimumcolumns for specified variables.
Usage
std_cum_min_augment(.data, .value, .names = "auto", .initial_value = 0)Arguments
.data | A data frame to augment. |
.value | A column name or names for which to compute the cumulative minimum. |
.names | Optional. A character vector of names for the new cumulativeminimum columns. Defaults to "auto", which generates names based on theoriginal column names. |
.initial_value | A numeric value to start the cumulative minimum from.Defaults to 0. |
Details
The function takes a data frame and a column name (or names) andcomputes the cumulative minimum for each specified column, starting from aninitial value. If the column names are not provided, it will throw an error.
Value
A tibble with the original data and additional columns containingthe cumulative minimums.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_prod_augment(),std_cum_sum_augment(),subset_walks()
Examples
df <- data.frame(x = c(5, 3, 8, 1, 4), y = c(10, 7, 6, 12, 5))std_cum_min_augment(df, .value = x)std_cum_min_augment(df, .value = y, .names = c("cummin_y"))Augment Cumulative Product
Description
This function augments a data frame by adding cumulative productcolumns for specified variables.
Usage
std_cum_prod_augment(.data, .value, .names = "auto", .initial_value = 1)Arguments
.data | A data frame to augment. |
.value | A column name or names for which to compute the cumulative product. |
.names | Optional. A character vector of names for the new cumulativeproduct columns. Defaults to "auto", which generates names based on the originalcolumn names. |
.initial_value | A numeric value to start the cumulative product from.Defaults to 1. |
Details
The function takes a data frame and a column name (or names) andcomputes the cumulative product for each specified column, starting from aninitial value. If the column names are not provided, it will throw an error.
Value
A tibble with the original data and additional columns containing thecumulative products.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_sum_augment(),subset_walks()
Examples
df <- data.frame(x = 1:5, y = 6:10)std_cum_prod_augment(df, .value = x)std_cum_prod_augment(df, .value = y, .names = c("cumprod_y"))Augment Cumulative Sum
Description
This function augments a data frame by adding cumulative sumcolumns for specified variables.
Usage
std_cum_sum_augment(.data, .value, .names = "auto", .initial_value = 0)Arguments
.data | A data frame to augment. |
.value | A column name or names for which to compute the cumulative sum. |
.names | Optional. A character vector of names for the new cumulativesum columns. Defaults to "auto", which generates names based on the originalcolumn names. |
.initial_value | A numeric value to start the cumulative sum from.Defaults to 0. |
Details
The function takes a data frame and a column name (or names) andcomputes the cumulative sum for each specified column, starting from aninitial value. If the column names are not provided, it will throw an error.
Value
A tibble with the original data and additional columns containingthe cumulative sums.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),subset_walks()
Examples
df <- data.frame(x = 1:5, y = 6:10)std_cum_sum_augment(df, .value = x)std_cum_sum_augment(df, .value = y, .names = c("cumsum_y"))Subset Walks by Extreme Values
Description
This function subsets random walks to identify the walk with themaximum or minimum value.
Usage
subset_walks(.data, .type = "max", .value = "y")Arguments
.data | A data frame containing random walks. It must have columns |
.type | A character string specifying the type of subset: "max" for maximum value, "min" for minimum value, or "both" for both maximum and minimum values. |
.value | A character string specifying the column name to use for finding extreme values. Defaults to "y". |
Details
Thesubset_walks function takes a data frame containing randomwalks and subsets it to return the walk with the maximum or minimum valuebased on the specified type. It requires that the input data frame containscolumnswalk_number and the specified value column.
Value
A data frame containing the subset walk.
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Utility Functions:confidence_interval(),convert_snake_to_title_case(),generate_caption(),get_attributes(),rand_walk_column_names(),rand_walk_helper(),running_quantile(),std_cum_max_augment(),std_cum_mean_augment(),std_cum_min_augment(),std_cum_prod_augment(),std_cum_sum_augment()
Examples
set.seed(123)df <- rw30()subset_walks(df, .type = "max")subset_walks(df, .type = "min")subset_walks(df, .type = "both")# Example with a specific value columnset.seed(123)discrete_walk() |> subset_walks(.type = "both", .value = "cum_sum_y") |> visualize_walks(.pluck = 2)Summarize Walks Data
Description
Summarizes random walk data by computing statistical measures.
Usage
summarize_walks(.data, .value, .group_var)summarise_walks(.data, .value, .group_var)Arguments
.data | A data frame or tibble containing random walk data. |
.value | A column name (unquoted) representing the value to summarize. |
.group_var | A column name (unquoted) representing the grouping variable. |
Details
This function requires that the input data frame contains acolumn named 'walk_number' and that the value to summarize is provided.It computes statistics such as mean, median, variance, and quantilesfor the specified value variable. #' This function summarizes a data framecontaining random walk data by computing various statistical measures for aspecified value variable, grouped by a specified grouping variable. It checksfor necessary attributes and ensures that the data frame is structured correctly.
Value
A tibble containing the summarized statistics for each group,including mean, median, range, quantiles, variance, standard deviation,and more.
Author(s)
Steven P. Sanderson II, MPH
Examples
library(dplyr)# Example data framewalk_data <- random_normal_walk(.initial_value = 100)# Summarize the walkssummarize_walks(walk_data, cum_sum_y, walk_number) |> glimpse()summarize_walks(walk_data, y) |> glimpse()# Example with missing value variable# summarize_walks(walk_data, NULL, group) # This will trigger an error.Visualize Walks
Description
visualize_walks() visualizes the output of the random walkfunctions in the RandomWalker package, resulting in one or more ggplot2 plotsput together in a patchwork composed of 1 or more patches.
Usage
visualize_walks(.data, .alpha = 0.7, .interactive = FALSE, .pluck = FALSE)Arguments
.data | The input data. Assumed to be created by one of the random walkfunctions in the RandomWalker package, but can be any data frame or tibblethat contains columns |
.alpha | The alpha value for all the line charts in the visualization.Values range from 0 to 1. Default is 0.7. |
.interactive | A boolean value. TRUE if you want the patches to beinteractive. FALSE if you don't. Default is FALSE. |
.pluck | If you want to visualize only one of the You can choose one ofthe values ( |
Details
visualize_walks() generates visualizations of the random walksgenerated by the random walk functions in the RandomWalker package. Theseare the functions at the moment of writing:
brownian_motion()
discrete_walk()
geometric_brownian_motion()
random_normal_drift_walk()
random_normal_walk()
rw30()
It is possible there are more when you read this, but you can check the restof the documentation for the current situation.
The visualization function is meant to be easy to use. No parameters needed,but you can set.alpha if the default value of 0.7 isn't to yourliking.
You can also choose whether you want the visualization to be interactive ornot by setting.interactive to TRUE. The function uses theggiraphpackage for making the patches interactive.
If you want to visualize only one of the attributes, you can choose use one ofthese values (y,cum_sum,cum_prod,cum_min,cum_max,cum_mean) forthe.pluck parameter.
Value
A patchwork composed of 1 or more patches
Author(s)
Antti Lennart Rask
Examples
# Generate random walks and visualize the resultset.seed(123)rw30() |> visualize_walks()# Set the alpha value to be other than the default 0.7set.seed(123)rw30() |> visualize_walks(.alpha = 0.5)# Use the function with an input that has alternatives for yset.seed(123)random_normal_walk(.num_walks = 5, .initial_value = 100) |> visualize_walks()# Use the function to create interactive visualizationsset.seed(123)random_normal_walk(.num_walks = 5, .initial_value = 100) |> visualize_walks(.interactive = TRUE)# Use .pluck to pick just one visualizationset.seed(123)random_normal_walk(.num_walks = 5, .initial_value = 100) |> visualize_walks(.pluck = c(1, 3))