> are these dummy implementations intended?
Yes. There is no state. The only parameter is the dimensionality which is a template parameter.
We do often serialize underlying helper distributions, in your case the normal distribution _M_n. While the normal distribution mean and stddev are trivial for your case (not actually needing serialization)
the normal distribution has these _M_saved, etc. shat we should store. So I would just serialize _M_n here. This is a great distribution. Thanks! Are you looking at the normal distribution equivalent of these?