Postprocess to samples from a moment-matched negative-binomial distribution

Use this function to postprocess samples from the forecast distribution to samples from a negative binomial distribution that was fitted by moment-matching (using mean and variance) to the input samples x. This is useful to convert samples generated via a different innovation_function like [draw_normal_with_zero_mean()] or [draw_bootstrap()] to a count distribution.

Usage

to_moment_matched_nbinom(x)

Arguments

x: Numeric vector of non-negative samples of at least length 2

Value

Numeric vector of length equal to x

Details

If the required forecast output are count data (as when forecasting the demand for products), this can be better than using round() or similar to preserve features of the forecast distribution.

Examples

x <- to_non_negative_with_identical_mean(
  stats::rnorm(n = 10000, mean = 5, sd = 3)
)
y <- to_moment_matched_nbinom(x = x)
summary(x); stats::var(x)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   0.000   2.953   4.911   4.974   6.853  17.089 
#> [1] 7.94514
summary(y); stats::var(y)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   0.000   3.000   5.000   4.928   7.000  19.000 
#> [1] 7.82657

# Forecasting simple count data

set.seed(992)
y <- stats::rnbinom(n = 50, mu = 3, size = 3/2)
model <- learn_weights(
  y = y,
  alphas_grid = list_sampled_alphas(
    n_target = 1000L,
    include_edge_cases = TRUE
  ),
  period_length = 12L,
  loss_function = loss_rmse
)

forecast <- predict(
  object = model,
  horizon = 12L,
  n_samples = 2501L,
  observation_driven = FALSE,
  innovation_function = draw_normal_with_zero_mean,
  postprocess = to_moment_matched_nbinom
)

forecast$paths[1:5, ]
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,]    1    1    5    1    4    3    1    1    0     0     2     2
#> [2,]    4    1    0    2    3    2    2    2    5     6     1     0
#> [3,]    8    3    0    6    1    2    0    5    1     2     2     0
#> [4,]    2    0    6    4    7    1    0    4    3     6     4     0
#> [5,]    1    1    6    3    1    7    5    2    4     4     5     2

if (require("ggplot2")) {
  autoplot(forecast)
  autoplot(forecast, method = "paths")
}