Generate Multiple Random Walks with Drift
Source:R/gen-random-normal-walk-drift.R
random_normal_drift_walk.RdThis function generates a specified number of random walks, each consisting of a specified number of steps. The steps are generated from a normal distribution with a given mean and standard deviation. An additional drift term is added to each step to introduce a consistent directional component to 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.
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).
Details
This function generates multiple random walks with a specified drift. Each walk is generated using a normal distribution for the steps, with an additional drift term added to each step.
See also
Other Generator Functions:
brownian_motion(),
custom_walk(),
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()
#> # A tibble: 2,500 × 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 -1.02 -1.02 0 -1.02 -1.02
#> 2 1 2 -0.821 -1.84 0 -1.02 -0.821
#> 3 1 3 2.63 0.785 0 -1.02 2.63
#> 4 1 4 1.31 2.09 0 -1.02 2.63
#> 5 1 5 1.60 3.69 0 -1.02 2.63
#> 6 1 6 5.00 8.69 0 -1.02 5.00
#> 7 1 7 4.30 13.0 0 -1.02 5.00
#> 8 1 8 1.41 14.4 0 -1.02 5.00
#> 9 1 9 1.41 15.8 0 -1.02 5.00
#> 10 1 10 1.30 17.1 0 -1.02 5.00
#> # ℹ 2,490 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
random_normal_drift_walk(.dimensions = 3) |>
head() |>
t()
#> [,1] [,2] [,3] [,4]
#> walk_number "1" "1" "1" "1"
#> step_number "1" "2" "3" "4"
#> x "-1.0209513" "-0.8208306" " 2.6267635" " 1.3090720"
#> y "-1.320813127" " 0.003360855" "-0.646906611" "-0.995299932"
#> z "4.497621" "5.023636" "3.280933" "4.732466"
#> cum_sum_x "-1.0209513" "-1.8417819" " 0.7849816" " 2.0940535"
#> cum_sum_y "-1.320813" "-1.317452" "-1.964359" "-2.959659"
#> cum_sum_z " 4.497621" " 9.521257" "12.802190" "17.534657"
#> cum_prod_x "0" "0" "0" "0"
#> cum_prod_y "0" "0" "0" "0"
#> cum_prod_z "0" "0" "0" "0"
#> cum_min_x "-1.020951" "-1.020951" "-1.020951" "-1.020951"
#> cum_min_y "-1.320813" "-1.320813" "-1.320813" "-1.320813"
#> cum_min_z "4.497621" "4.497621" "3.280933" "3.280933"
#> cum_max_x "-1.0209513" "-0.8208306" " 2.6267635" " 2.6267635"
#> cum_max_y "-1.320813127" " 0.003360855" " 0.003360855" " 0.003360855"
#> cum_max_z "4.497621" "5.023636" "5.023636" "5.023636"
#> cum_mean_x "-1.0209513" "-0.9208910" " 0.2616605" " 0.5235134"
#> cum_mean_y "-1.3208131" "-0.6587261" "-0.6547863" "-0.7399147"
#> cum_mean_z "4.497621" "4.760628" "4.267397" "4.383664"
#> [,5] [,6]
#> walk_number "1" "1"
#> step_number "5" "6"
#> x " 1.5971390" " 4.9979813"
#> y "-2.450994467" "-1.489431349"
#> z "3.460592" "3.022439"
#> cum_sum_x " 3.6911926" " 8.6891739"
#> cum_sum_y "-5.410653" "-6.900085"
#> cum_sum_z "20.995249" "24.017688"
#> cum_prod_x "0" "0"
#> cum_prod_y "0" "0"
#> cum_prod_z "0" "0"
#> cum_min_x "-1.020951" "-1.020951"
#> cum_min_y "-2.450994" "-2.450994"
#> cum_min_z "3.280933" "3.022439"
#> cum_max_x " 2.6267635" " 4.9979813"
#> cum_max_y " 0.003360855" " 0.003360855"
#> cum_max_z "5.023636" "5.023636"
#> cum_mean_x " 0.7382385" " 1.4481956"
#> cum_mean_y "-1.0821307" "-1.1500141"
#> cum_mean_z "4.199050" "4.002948"