Generate Multiple Random Weibull Walks in Multiple Dimensions
Source:R/gen-random-weibull-walk.R
random_weibull_walk.RdA Weibull random walk is a stochastic process in which each step is drawn from the Weibull distribution, a flexible distribution commonly used to model lifetimes, reliability, and extreme values. This function allows for the simulation of multiple independent random walks in one, two, or three dimensions, with user control over the number of walks, steps, and the shape and scale parameters of the Weibull distribution. Sampling options allow for further customization, including the ability to sample a proportion of steps and to sample with or without replacement. The resulting data frame includes cumulative statistics for each walk, making it suitable for simulation studies 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.
Value
A data frame with the random walks and cumulative statistics as columns.
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).
Details
The random_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 the
Weibull distribution using stats::rweibull(). The user can specify the
number of walks, the number of steps in each walk, and the parameters
.shape and .scale for the Weibull distribution. The function also allows
for sampling a proportion of the steps and optionally sampling with replacement.
See also
Other Generator Functions:
brownian_motion(),
discrete_walk(),
geometric_brownian_motion(),
random_normal_drift_walk(),
random_normal_walk(),
random_smirnov_walk(),
random_t_walk(),
random_uniform_walk(),
random_wilcox_walk()
Other Continuous Distribution:
brownian_motion(),
geometric_brownian_motion(),
random_normal_drift_walk(),
random_normal_walk(),
random_t_walk(),
random_uniform_walk()
Examples
set.seed(123)
random_weibull_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 0.422 0.422 0 0.422 0.422
#> 2 1 2 0.816 1.24 0 0.422 0.816
#> 3 1 3 0.367 1.61 0 0.367 0.816
#> 4 1 4 0.121 1.73 0 0.121 0.816
#> 5 1 5 0.103 1.83 0 0.103 0.816
#> 6 1 6 0.422 2.25 0 0.103 0.816
#> 7 1 7 0.0152 2.27 0 0.0152 0.816
#> 8 1 8 3.70 5.97 0 0.0152 3.70
#> 9 1 9 1.46 7.43 0 0.0152 3.70
#> 10 1 10 1.92 9.35 0 0.0152 3.70
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
random_weibull_walk(.dimensions = 3) |>
head() |>
t()
#> [,1] [,2] [,3] [,4] [,5]
#> walk_number "1" "1" "1" "1" "1"
#> step_number "1" "2" "3" "4" "5"
#> x "0.4220431" "0.8159928" "0.3670090" "0.1205091" "0.1028093"
#> y "2.84802700" "0.61234101" "0.08808446" "0.48069865" "2.90718840"
#> z "1.02706319" "0.55112373" "7.67272276" "1.53631719" "0.05063955"
#> cum_sum_x "0.4220431" "1.2380359" "1.6050449" "1.7255540" "1.8283632"
#> cum_sum_y "2.848027" "3.460368" "3.548452" "4.029151" "6.936340"
#> cum_sum_z " 1.027063" " 1.578187" " 9.250910" "10.787227" "10.837866"
#> cum_prod_x "0" "0" "0" "0" "0"
#> cum_prod_y "0" "0" "0" "0" "0"
#> cum_prod_z "0" "0" "0" "0" "0"
#> cum_min_x "0.4220431" "0.4220431" "0.3670090" "0.1205091" "0.1028093"
#> cum_min_y "2.84802700" "0.61234101" "0.08808446" "0.08808446" "0.08808446"
#> cum_min_z "1.02706319" "0.55112373" "0.55112373" "0.55112373" "0.05063955"
#> cum_max_x "0.4220431" "0.8159928" "0.8159928" "0.8159928" "0.8159928"
#> cum_max_y "2.848027" "2.848027" "2.848027" "2.848027" "2.907188"
#> cum_max_z "1.027063" "1.027063" "7.672723" "7.672723" "7.672723"
#> cum_mean_x "0.4220431" "0.6190180" "0.5350150" "0.4313885" "0.3656726"
#> cum_mean_y "2.848027" "1.730184" "1.182817" "1.007288" "1.387268"
#> cum_mean_z "1.0270632" "0.7890935" "3.0836366" "2.6968067" "2.1675733"
#> [,6]
#> walk_number "1"
#> step_number "6"
#> x "0.4220431"
#> y "0.72972278"
#> z "0.20846750"
#> cum_sum_x "2.2504063"
#> cum_sum_y "7.666062"
#> cum_sum_z "11.046334"
#> cum_prod_x "0"
#> cum_prod_y "0"
#> cum_prod_z "0"
#> cum_min_x "0.1028093"
#> cum_min_y "0.08808446"
#> cum_min_z "0.05063955"
#> cum_max_x "0.8159928"
#> cum_max_y "2.907188"
#> cum_max_z "7.672723"
#> cum_mean_x "0.3750677"
#> cum_mean_y "1.277677"
#> cum_mean_z "1.8410557"