Check transformation domain in `TransformedDistribution` constructor?

[dylanhmorris]

Feature Summary

Distributions know their support. Transformations know their domain and codomain. As far as I can tell, it should therefore be possible to confirm that a transformation used in constructing a TransformedDistribution from a base distribution has a domain equal to the support of the base distribution, and error if not.

Why is this needed?

The lack of an error here can lead to unexpected and somewhat opaque behavior. See e.g. #1756

Questions

• Is there reason to allow the creation of TransformedDistributions with a transformation whose domain is not equal to the base distribution's support?
• Are there barriers to implementation that I'm not seeing?

Happy to take this on if it would be valuable.