I was going through the Zero Inflated Distribution source code and I noticed that there is assert base_dist.support.is_discrete line in the code. Is this line necessary. Can i just comment it out and plug a continuous distribution in the code instead of something like Poisson or NegativeBinomial. Drawing samples seems to be fine but if i use the zero inflated distribution along with a continuous base distribution and do an MLE is it wrong in principal.
this will likely lead to incorrect inferences.
mixed support distributions get tricky in terms of measure theory etc see e.g. here