Distribution Proposal: Truncated SkewNormal

[ericmjl]

@ricardoV94, I'm wondering what would it take to implement a Truncated SkewNormal distribution?

The main use case I have is to use it to construct unimodal posterior approximations.

SkewNormal is necessary if we want to model posteriors that are skewed off from a Gaussian-like shape.

Truncated is necessary if we want to approximate bound posteriors, i.e. things that are positive-only.

Do you have guidance here?

[ricardoV94]

We want to implement a general truncation solution that works for any distribution, similar to the general censored API we have now. The machinary would probably be implemented in Aeppl: aesara-devs/aeppl#96

For an immediate solution all you need is the CDF of the skewnormal and you can implement it with an extra potential term and interval transform

[ricardoV94]

This should now be available with pm.Truncated assuming the logcdf is implemented for the SkewNormal