hurdles and zero inflated distributions

[njtierney]

After discussing with Francis Hui, the key ideas are as follows:

• zero inflation means a distribution of 0s, plus a distribution that might already contain 0s.
• truncation means a distribution of 0s, plus a truncated distribution of 1 onwards.

[hrlai]

Great to see continued interest in this module! Just want to quickly refer back to #15 and #17 . Both PRs indeed parameterise zero inflation like you and Francis described above, e.g.:

greta.distributions/R/zero_inflated_negative_binomial.R

Lines 51 to 54 in 6a6ab7b

	zi <- binom$sample(seed = seed)
	lbd <- negbin$sample(seed = seed)
	(fl(1) - zi) * lbd

Also to note that in glmmTMB the distribution families with truncated_* prefixes are for hurdle models, i.e., they are truncated at 1. I think this is their design philosophy. Also note that Francis' boral package has the zero-truncated version of Poisson and negative binomial: https://rdrr.io/cran/boral/man/about.distributions.html as family = zt*

Hopefully these notes help to tidy up things.

[njtierney]

Thanks for that, @hrlai !

We've got a few other priorities at the moment with getting TF2 greta onto CRAN and the variety of issues around that. Hopefully that goes ahead quickly and I can focus my attention on this. Really keen to make it easy to add new and useful distributions to greta!