David Widmann

> Beyond the PDS requirement, PDMats has the unusual approach "allocate no matter what". This pops up quite regularly, I think it would be good to add support for an...

Yeah, unfortunately the test setup is a bit of a mess, mostly due to historical reasons. Since `NegativeBinomial` is already checked with the values from R, I think a good...

> MGF are not necessarily defined on the whole Real/Complex domain, what should be returned when getting a value out of bound? NaN or ArgumentError ? I was wondering the...

You can specify the mixture weights as an additional argument. Some examples are shown in https://juliastats.org/Distributions.jl/stable/mixture/#Constructors.

I assume the motivation for `convert` here is that `quantile` should return values that can be sampled from the distribution of interest and are in its support. However, for discrete...

There are multiple (open and closed) issues about this behaviour: e.g. https://github.com/JuliaStats/Distributions.jl/issues/1071 and linked issues. Generally, the parameters are just treated as parameters, distinct from the type of the samples....

That is not required. I found a fix (and a bug on the way) without it.

Basically, - we can eliminate the special case branch alltogether by using `xlogy` and `xlog1py` - we just have to fix the derivatives of these functions, defined in DiffRules and...

Sure. I guess the same could be done for (some) characteristic functions as well (https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)#Entire_characteristic_functions).

This CR definition is wrong, it is missing the derivatives with respect to `d`. I would have suggested `gradlogpdf` but I assumed you would like to get the gradient with...