Zero-and-One-Adjusted Beta

[neverfox]

Very cool to see the addition of the zero-adjusted/inflated distributions. Would it be practically possible to have a zero-and-one-adjusted/inflated Beta, i.e. ZOIB, a Beta that allows the response to be [0, 1]? This goes towards the idea of using it with binary classification responses and getting, instead of the usual, natural p parameter of a Bernoulli, the distribution of p itself as a Beta distribution. This would be interesting to ask probabilistic questions about the predicted probability, I think. I could probably hack it by modifying the data with a small epsilon, but it ZABeta opens the door to doing that in a principled way. I think the idea would mean:

• A gate/probability, given by a Bernoulii, of a 0 or 1
• A gate/probability, given by a Bernoulii, of a 0 (or 1, if you like) given that it's 0 or 1
• The beta that models the outcome between 0 and 1 if it’s not zero or not one

[StatMixedML]

Thanks for your detailed outline.

Extending the current Beta distribution from (0,1) to

• ZABeta [0,1)
• OABeta (0,1]
• ZOABeta [0,1]

is on the ToDo already.

[Pranavesh-Panakkal]

Hi, I see ZABeta() is already implemented. Could you give some guidance on how to model ZOIB (ZOABeta)? Thanks.