Generate Multiple Random Cauchy Walks in Multiple Dimensions
Source:R/gen-random-cauchy-walk.R
random_cauchy_walk.RdThe random_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 the
parameters of the Cauchy distribution (location and scale). The function
also 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
.nto sample. Default is 0.8.- .dimensions
An integer specifying the number of dimensions (1, 2, or 3). Default is 1.
Value
A tibble containing the generated random walks with columns depending on the number of dimensions:
walk_number: Factor representing the walk number.step_number: Step index.y: If.dimensions = 1, the value of the walk at each step.x,y: If.dimensions = 2, the values of the walk in two dimensions.x,y,z: If.dimensions = 3, the values of the walk in three dimensions.
The following are also returned based upon how many dimensions there are and could be any of x, y and or z:
cum_sum: Cumulative sum 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.
Details
The location and scale 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.
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()
#> # A tibble: 2,000 × 8
#> walk_number step_number y cum_sum_y cum_prod_y cum_min_y cum_max_y
#> <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 1.27 1.27 0 1.27 1.27
#> 2 1 2 -0.784 0.485 0 -0.784 1.27
#> 3 1 3 3.40 3.89 0 -0.784 3.40
#> 4 1 4 -0.385 3.50 0 -0.784 3.40
#> 5 1 5 -0.189 3.31 0 -0.784 3.40
#> 6 1 6 0.144 3.46 0 -0.784 3.40
#> 7 1 7 -11.3 -7.84 0 -11.3 3.40
#> 8 1 8 -0.351 -8.19 0 -11.3 3.40
#> 9 1 9 -6.13 -14.3 0 -11.3 3.40
#> 10 1 10 7.29 -7.03 0 -11.3 7.29
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
random_cauchy_walk(.dimensions = 3, .location = c(0, 1, 2), .scale = c(1, 2, 3)) |>
head() |>
t()
#> [,1] [,2] [,3] [,4]
#> walk_number "1" "1" "1" "1"
#> step_number "1" "2" "3" "4"
#> x " 1.2691296" "-0.7842432" " 3.4011811" "-0.3850032"
#> y " 2.9213852" "-2.4294558" " 8.5571019" "-0.5695959"
#> z "-413.258437" " 8.070792" " -3.888510" " 9.224272"
#> cum_sum_x "1.2691296" "0.4848863" "3.8860675" "3.5010642"
#> cum_sum_y " 2.9213852" " 0.4919294" " 9.0490313" " 8.4794355"
#> cum_sum_z "-413.2584" "-405.1876" "-409.0762" "-399.8519"
#> cum_prod_x "0" "0" "0" "0"
#> cum_prod_y "0" "0" "0" "0"
#> cum_prod_z "0" "0" "0" "0"
#> cum_min_x " 1.2691296" "-0.7842432" "-0.7842432" "-0.7842432"
#> cum_min_y " 2.921385" "-2.429456" "-2.429456" "-2.429456"
#> cum_min_z "-413.2584" "-413.2584" "-413.2584" "-413.2584"
#> cum_max_x "1.269130" "1.269130" "3.401181" "3.401181"
#> cum_max_y " 2.921385" " 2.921385" " 8.557102" " 8.557102"
#> cum_max_z "-413.258437" " 8.070792" " 8.070792" " 9.224272"
#> cum_mean_x "1.2691296" "0.2424432" "1.2953558" "0.8752661"
#> cum_mean_y "2.9213852" "0.2459647" "3.0163438" "2.1198589"
#> cum_mean_z "-413.25844" "-202.59382" "-136.35872" " -99.96297"
#> [,5] [,6]
#> walk_number "1" "1"
#> step_number "5" "6"
#> x "-0.1892392" " 0.1441052"
#> y " 1.6697976" "10.6412732"
#> z " 8.145512" " -26.240418"
#> cum_sum_x "3.3118250" "3.4559303"
#> cum_sum_y "10.1492330" "20.7905062"
#> cum_sum_z "-391.7064" "-417.9468"
#> cum_prod_x "0" "0"
#> cum_prod_y "0" "0"
#> cum_prod_z "0" "0"
#> cum_min_x "-0.7842432" "-0.7842432"
#> cum_min_y "-2.429456" "-2.429456"
#> cum_min_z "-413.2584" "-413.2584"
#> cum_max_x "3.401181" "3.401181"
#> cum_max_y " 8.557102" "10.641273"
#> cum_max_z " 9.224272" " 9.224272"
#> cum_mean_x "0.6623650" "0.5759884"
#> cum_mean_y "2.0298466" "3.4650844"
#> cum_mean_z " -78.34127" " -69.65780"