I need to interpolate between the given points.

Now, of course there is not a unique interpolation, but I guess there is a maximum entropy interpolation that is in some sense closest to a Gaussian. I wonder how I would find out what it is.

Secondly, I would like to find distributions of the sum of two such distributions. I am imagining a Monte Carlo method would work, but if there is a closed form, so much the better. It needs to be reasonably computationally efficient and either available as a Python package or relatively easily programmed and tested.

Thirdly, similarly for a product of two such distributions.

If there is not a closed form, I need a way to take samples of the distribution from Python. It's not hard for me to construct a method that is crudely correct in the sense that the biases are unlikely to matter for the purposes at hand, but it seems someone ought to be able to tell me how to do better.

It would be nearly hopeless for a small traffic blog like this to get an answer by itself, but I wonder if Twitter isn't going to prove useful for scientists to answer questions of this sort. So I've tweeted a call for assistance and pointed to this posting. It will be very encouraging if I get a useful response; I have little hangups like this one all the time.