A Poisson random walk is a stochastic process in which each step is drawn from the Poisson distribution, commonly used for modeling count data. 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 lambda parameter for the 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_poisson_walk(
.num_walks = 25,
.n = 100,
.lambda = 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
Integer. Number of random variables to return for each walk. Default is 100.
- .lambda
Numeric or vector. Mean(s) for the Poisson 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 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_poisson_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 Poisson distribution using base::rpois(). The user
can specify the number of samples in each walk (n), the lambda parameter for
the Poisson distribution, and the number of dimensions. 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_hypergeometric_walk(),
random_logistic_walk(),
random_lognormal_walk(),
random_multinomial_walk(),
random_negbinomial_walk(),
random_normal_drift_walk(),
random_normal_walk(),
random_smirnov_walk(),
random_t_walk(),
random_uniform_walk(),
random_weibull_walk(),
random_wilcox_walk(),
random_wilcoxon_sr_walk()
Other Discrete Distribution:
discrete_walk(),
random_hypergeometric_walk(),
random_multinomial_walk(),
random_negbinomial_walk(),
random_smirnov_walk(),
random_wilcox_walk(),
random_wilcoxon_sr_walk()
Examples
set.seed(123)
random_poisson_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> <int> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 1 1 0 1 1
#> 2 1 2 1 2 0 1 1
#> 3 1 3 1 3 0 1 1
#> 4 1 4 2 5 0 1 2
#> 5 1 5 2 7 0 1 2
#> 6 1 6 1 8 0 1 2
#> 7 1 7 4 12 0 1 4
#> 8 1 8 0 12 0 0 4
#> 9 1 9 0 12 0 0 4
#> 10 1 10 0 12 0 0 4
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
random_poisson_walk(.dimensions = 3, .lambda = c(1, 2, 3)) |>
head() |>
t()
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> walk_number "1" "1" "1" "1" "1" "1"
#> step_number "1" "2" "3" "4" "5" "6"
#> x "1" "1" "1" "4" "4" "1"
#> y "1" "2" "4" "3" "0" "1"
#> z "2" "3" "0" "2" "3" "3"
#> cum_sum_x " 1" " 2" " 3" " 7" "11" "12"
#> cum_sum_y " 1" " 3" " 7" "10" "10" "11"
#> cum_sum_z " 2" " 5" " 5" " 7" "10" "13"
#> cum_prod_x "0" "0" "0" "0" "0" "0"
#> cum_prod_y "0" "0" "0" "0" "0" "0"
#> cum_prod_z "0" "0" "0" "0" "0" "0"
#> cum_min_x "1" "1" "1" "1" "1" "1"
#> cum_min_y "1" "1" "1" "1" "0" "0"
#> cum_min_z "2" "2" "0" "0" "0" "0"
#> cum_max_x "1" "1" "1" "4" "4" "4"
#> cum_max_y "1" "2" "4" "4" "4" "4"
#> cum_max_z "2" "3" "3" "3" "3" "3"
#> cum_mean_x "1.00" "1.00" "1.00" "1.75" "2.20" "2.00"
#> cum_mean_y "1.000000" "1.500000" "2.333333" "2.500000" "2.000000" "1.833333"
#> cum_mean_z "2.000000" "2.500000" "1.666667" "1.750000" "2.000000" "2.166667"