Calculate Average Distribution from Multiple Distributional Objects

Source: R/sim-plots.R

Compute a single "average" distribution from a vector of distributional objects. This function calculates the mean of each hyperparameter across all input distributions and returns a new distributional object of the same family with these averaged hyperparameters.

avg_dist(x)

Arguments

x

A vector of distributional objects of the same family (beta, normal, multivariate normal, or mixture).

Value

A single distributional object of the same family as the input, with hyperparameters set equal to the average of all input distribution hyperparameters.

Details

The function supports four distribution families:

  • Beta distributions: Averages the shape1 and shape2 hyperparameters

  • Normal distributions: Averages the mean and standard deviation hyperparameters

  • Multivariate normal distributions: Averages the location vectors and covariance matrices

  • Mixture distributions: Same as above for each distribution type, where averaging is done by component. Also averages the mixture weight.

For multivariate normal distributions, both the location vector and covariance matrix are averaged element-wise.

Examples

library(distributional)

# Beta distributions
beta_dists <- c(
  dist_beta(shape1 = 2, shape2 = 5),
  dist_beta(shape1 = 3, shape2 = 3),
  dist_beta(shape1 = 4, shape2 = 2)
)
avg_dist(beta_dists) |> parameters()
#>   shape1   shape2
#> 1      3 3.333333

# Normal distributions
norm_dists <- c(
  dist_normal(mu = 0, sigma = 1),
  dist_normal(mu = 2, sigma = 2),
  dist_normal(mu = 4, sigma = 3)
)
avg_dist(norm_dists) |> parameters()
#>   mu sigma
#> 1  2     2

# Multivariate normal distributions
mvn_dists <- c(
  dist_multivariate_normal(mu = list(c(0, 0)), sigma = list(matrix(c(1, 0, 0, 1), nrow = 2))),
  dist_multivariate_normal(mu = list(c(1, 1)), sigma = list(matrix(c(2, 0, 0, 2), nrow = 2)))
)
avg_dist(mvn_dists) |> parameters()
#>         mu              sigma
#> 1 0.5, 0.5 1.5, 0.0, 0.0, 1.5