MeanParametersSpace is not actually mean parametrization

[Nimrais]

By mean paramtrization people in statistics mean the following if we have an exponential distribution with sufficient statistics T then mean parameters $\mu$ are such parameters that $\mu = \mathbb{E}[T(x)]$. It does not hold for MeanParametersSpace. By MeanParametersSpace as I understood we mean parameterization in Distributions.jl but then it should be called differently.

There is a branch that tests this property $\mu = \mathbb{E}[T(x)]$ for many distributions it obviously fails bf7de35.

[Nimrais]

For example check this note from D. M. Blei https://www.cs.princeton.edu/courses/archive/fall11/cos597C/lectures/exponential-families.pdf.

[Nimrais]

Probably it should be named BaseDistributionParametrization.

[bvdmitri]

I see your point, I wouldn't change the naming convention too much though, maybe BaseParametersSpace or DefaultParametersSpace?

[Nimrais]

Yeah, I think you have a point DefaultParametersSpace or BaseParamersSpace both sound good for me.