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Generate Multiple Random Walks with Drift

Source: R/gen-random-normal-walk-drift.R
random_normal_drift_walk.Rd

This 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
)

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.

Value

A tibble in long format with columns walk_number, x (step index), and y (walk value). The tibble has attributes for the number of walks, number of steps, mean, standard deviation, and drift.

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(), discrete_walk(), geometric_brownian_motion(), random_normal_walk()

Author

Steven P. Sanderson II, MPH

Examples

library(ggplot2)

set.seed(123)
walks <- random_normal_drift_walk(.num_walks = 10, .n = 50, .mu = 0, .sd = 1.2,
                                  .drift = 0.05)
ggplot(walks, aes(x = x, y = y, group = walk_number, color = walk_number)) +
  geom_line() +
  labs(title = "Random Walks with Drift", x = "Time", y = "Value") +
  theme_minimal() +
  theme(legend.position = "none")