family() to optionally return the types of distributions in the mixture

[statasaurus]

At the moment, there really isn't an easy way of looking at the contents of mixture distributions. I am trying to determine if all the elements in a mixture are normal to see if I can just use conjugacy to calculate the posterior. But, family() just returns the that it is a mixture. So it would be good if there was maybe an additional parameter or something that you could add to family() to look at the distributions making up the mixture.

---

Brief description of the problem

x <- dist_mixture(dist_normal(0, 1), dist_normal(5, 2), weights = c(0.3, 0.7))
family(x)
foo <- vec_data(x)
foo[[1]]$dist |> 
  map_lgl(\(x) "dist_normal" %in% class(x))

[mitchelloharawild]

This seems a bit tricky to design, but a similar problem would apply to other distribution modifiers - dist_inflated(), dist_truncated(), and dist_transformed().

Here's a recursive approach:

library(distributional)
x <- dist_mixture(dist_normal(0, 1), dist_normal(5, 2), weights = c(0.3, 0.7))

get_base_families <- function(x) {
  fam <- family(x)
  is_modified <- family(x) %in% c("mixture", "transformed", "inflated", "truncated")
  if(any(is_modified)) {
    fam[is_modified] <- lapply(parameters(x[is_modified])$dist, function(dist) lapply(dist, get_base_families))
  }
  fam
}

get_base_families(x)
#> [[1]]
#> [[1]][[1]]
#> [1] "normal"
#> 
#> [[1]][[2]]
#> [1] "normal"

^{Created on 2024-05-15 with reprex v2.0.2}

[statasaurus]

Something like this in the package would be super helpful. Thank you