Generate Multiple Random t-Distributed Walks in Multiple Dimensions
Source:R/gen-random-t-walk.R
random_t_walk.RdThe random_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 the
degrees of freedom for the t-distribution. The function
also 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
.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:
walk_number: Factor representing the walk number.x: Step index.y: t-distribution values.cum_sum: Cumulative sum ofy.cum_prod: Cumulative product ofy.cum_min: Cumulative minimum ofy.cum_max: Cumulative maximum ofy.
The tibble includes attributes for the function parameters.
Details
This function is a flexible generator for random walks where each step is drawn from a 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 of rt() from base R, which sets ncp = 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.
See also
Other Generator Functions:
brownian_motion(),
discrete_walk(),
geometric_brownian_motion(),
random_normal_drift_walk(),
random_normal_walk(),
random_smirnov_walk(),
random_uniform_walk(),
random_weibull_walk(),
random_wilcox_walk()
Other Continuous Distribution:
brownian_motion(),
geometric_brownian_motion(),
random_normal_drift_walk(),
random_normal_walk(),
random_uniform_walk(),
random_weibull_walk()
Examples
set.seed(123)
random_t_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 1.63 1.63 0 1.63 1.63
#> 2 1 2 -0.201 1.43 0 -0.201 1.63
#> 3 1 3 -1.18 0.243 0 -1.18 1.63
#> 4 1 4 -1.56 -1.31 0 -1.56 1.63
#> 5 1 5 1.49 0.176 0 -1.56 1.63
#> 6 1 6 1.85 2.03 0 -1.56 1.85
#> 7 1 7 0.849 2.87 0 -1.56 1.85
#> 8 1 8 -0.0532 2.82 0 -1.56 1.85
#> 9 1 9 0.819 3.64 0 -1.56 1.85
#> 10 1 10 -0.186 3.45 0 -1.56 1.85
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
random_t_walk(.dimensions = 3) |>
head() |>
t()
#> [,1] [,2] [,3] [,4]
#> walk_number "1" "1" "1" "1"
#> step_number "1" "2" "3" "4"
#> x " 1.6277162" "-0.2008853" "-1.1841513" "-1.5574288"
#> y "-2.2621208" "-2.7235161" "-0.2551528" " 1.1082730"
#> z " 1.2219381" " 1.4370475" "-1.6094411" "-0.5404590"
#> cum_sum_x " 1.6277162" " 1.4268309" " 0.2426796" "-1.3147493"
#> cum_sum_y "-2.262121" "-4.985637" "-5.240790" "-4.132517"
#> cum_sum_z "1.2219381" "2.6589856" "1.0495445" "0.5090855"
#> cum_prod_x "0" "0" "0" "0"
#> cum_prod_y "0" "0" "0" "0"
#> cum_prod_z "0" "0" "0" "0"
#> cum_min_x " 1.6277162" "-0.2008853" "-1.1841513" "-1.5574288"
#> cum_min_y "-2.262121" "-2.723516" "-2.723516" "-2.723516"
#> cum_min_z " 1.221938" " 1.221938" "-1.609441" "-1.609441"
#> cum_max_x "1.627716" "1.627716" "1.627716" "1.627716"
#> cum_max_y "-2.2621208" "-2.2621208" "-0.2551528" " 1.1082730"
#> cum_max_z "1.221938" "1.437048" "1.437048" "1.437048"
#> cum_mean_x " 1.62771622" " 0.71341546" " 0.08089319" "-0.32868732"
#> cum_mean_y "-2.262121" "-2.492818" "-1.746930" "-1.033129"
#> cum_mean_z "1.22193807" "1.32949281" "0.34984816" "0.12727137"
#> [,5] [,6]
#> walk_number "1" "1"
#> step_number "5" "6"
#> x " 1.4908605" " 1.8491933"
#> y "-1.7036063" "-1.0350036"
#> z " 0.6329316" "-0.6073508"
#> cum_sum_x " 0.1761113" " 2.0253045"
#> cum_sum_y "-5.836123" "-6.871127"
#> cum_sum_z "1.1420170" "0.5346663"
#> cum_prod_x "0" "0"
#> cum_prod_y "0" "0"
#> cum_prod_z "0" "0"
#> cum_min_x "-1.5574288" "-1.5574288"
#> cum_min_y "-2.723516" "-2.723516"
#> cum_min_z "-1.609441" "-1.609441"
#> cum_max_x "1.627716" "1.849193"
#> cum_max_y " 1.1082730" " 1.1082730"
#> cum_max_z "1.437048" "1.437048"
#> cum_mean_x " 0.03522225" " 0.33755076"
#> cum_mean_y "-1.167225" "-1.145188"
#> cum_mean_z "0.22840341" "0.08911104"