Generate Multiple Random Negative Binomial Walks
Source:R/gen-random-nbinomial-walk.R
random_negbinomial_walk.RdA Negative Binomial random walk is a stochastic process in which each step is drawn from the Negative Binomial distribution, commonly used for modeling count data with overdispersion. 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 distribution parameters. 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_negbinomial_walk(
.num_walks = 25,
.n = 100,
.size = 1,
.prob = 0.5,
.mu = NULL,
.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.
- .size
Integer. Number of successful trials or dispersion parameter. Default is 1. This must also match the number of dimensions, for example if
.dimensions = 3, then .size must be a vector of length 3 likec(1, 2, 3).- .prob
Numeric. Probability of success in each trial (0 < prob <= 1). Default is 0.5. This must also match the number of dimensions, for example if
.dimensions = 3, then .prob must be a vector of length 3 likec(0.5, 0.7, 0.9).- .mu
Numeric. Alternative parametrization via mean. Default is NULL. This must also match the number of dimensions, for example if
.dimensions = 3, then .mu must be a vector of length 3 likec(1, 2, 3).- .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_negbinomial_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 Negative Binomial distribution using stats::rnbinom().
The user can specify the number of samples in each walk (n), the size parameter,
the probability of success (prob), and/or the mean (mu), 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_normal_drift_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 Discrete Distribution:
discrete_walk(),
random_hypergeometric_walk(),
random_multinomial_walk(),
random_poisson_walk(),
random_smirnov_walk(),
random_wilcox_walk(),
random_wilcoxon_sr_walk()
Examples
set.seed(123)
random_negbinomial_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 0 0 0 0 0
#> 2 1 2 1 1 0 0 1
#> 3 1 3 0 1 0 0 1
#> 4 1 4 1 2 0 0 1
#> 5 1 5 2 4 0 0 2
#> 6 1 6 1 5 0 0 2
#> 7 1 7 1 6 0 0 2
#> 8 1 8 1 7 0 0 2
#> 9 1 9 1 8 0 0 2
#> 10 1 10 0 8 0 0 2
#> # ℹ 1,990 more rows
#> # ℹ 1 more variable: cum_mean_y <dbl>
set.seed(123)
random_negbinomial_walk(.dimensions = 3,
.size = c(1,2,3),
.prob = c(0.5,0.7,0.9)
) |>
head() |>
t()
#> [,1] [,2] [,3] [,4] [,5]
#> walk_number "1" "1" "1" "1" "1"
#> step_number "1" "2" "3" "4" "5"
#> x "0" "1" "0" "1" "2"
#> y "0" "2" "1" "2" "0"
#> z "1" "1" "0" "0" "1"
#> cum_sum_x "0" "1" "1" "2" "4"
#> cum_sum_y "0" "2" "3" "5" "5"
#> cum_sum_z "1" "2" "2" "2" "3"
#> 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" "0" "0" "0" "0"
#> cum_min_y "0" "0" "0" "0" "0"
#> cum_min_z "1" "1" "0" "0" "0"
#> cum_max_x "0" "1" "1" "1" "2"
#> cum_max_y "0" "2" "2" "2" "2"
#> cum_max_z "1" "1" "1" "1" "1"
#> cum_mean_x "0.0000000" "0.5000000" "0.3333333" "0.5000000" "0.8000000"
#> cum_mean_y "0.000000" "1.000000" "1.000000" "1.250000" "1.000000"
#> cum_mean_z "1.0000000" "1.0000000" "0.6666667" "0.5000000" "0.6000000"
#> [,6]
#> walk_number "1"
#> step_number "6"
#> x "1"
#> y "2"
#> z "0"
#> cum_sum_x "5"
#> cum_sum_y "7"
#> cum_sum_z "3"
#> cum_prod_x "0"
#> cum_prod_y "0"
#> cum_prod_z "0"
#> cum_min_x "0"
#> cum_min_y "0"
#> cum_min_z "0"
#> cum_max_x "2"
#> cum_max_y "2"
#> cum_max_z "1"
#> cum_mean_x "0.8333333"
#> cum_mean_y "1.166667"
#> cum_mean_z "0.5000000"