[LolWolf]

Also, gaussians are great approximations for large n, too, since the convolution of any distribution with itself n times (for n "large enough") is close to gaussian (by the CLT. More generally, there are very nice error estimates for many distributions).

I suspect this analysis can be carried out and yield quite good results in the gaussian case (a careful analysis might even yield error bounds on the result).

[theoh]

Yes. If you spend your whole life on one long multi-transfer bus journey, you'll end up with a gaussian.

It's a bit less clear that gaussians should be used when e.g. fitting a coordinate to an astronomical feature, which might not actually be symmetrical.

The other useful property that the gaussian has is its separability, in the 2D case. That is unique to the gaussian and counts for a lot.

[LolWolf]

Eh, I don’t think that many are required. Convergence to a Gaussian is pretty fast (you should check out page 299 of [0]), at four or five a Gaussian is already a quite good approximations.

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[0] https://www.dartmouth.edu/~chance/teaching_aids/books_articl...