As I recall the Gaussian distributions are the only distribution that have the desired property (i.e. form a monoid). While the Gaussian is important it is by far the only distribution of interest in machine learning. I would like to hear what the author has to say about handling, for example, the beta distribution.
In summary: interesting idea but I'm not sure it applies outside a very narrow domain.
In summary: interesting idea but I'm not sure it applies outside a very narrow domain.